Канал: Prof Ashwani Goyal

State and prove Roll’s Theorem | Geometrical Interpretation Of Roll’s Theorem | Lecture-1

State and prove Roll’s Theorem | Geometrical Interpretation Of Roll’s Theorem | Lecture-1

Laplace Transforms Of Integral | Theorems and Examples | Lecture-12

Laplace Transforms Of Integral | Theorems and Examples | Lecture-12

Derivatives of inverse hyperbolic functions | Results and Examples

Derivatives of inverse hyperbolic functions | Results and Examples

Graphs of Inverse hyperbolic functions and relation between logarithmic and inverse hyperbolic func

Graphs of Inverse hyperbolic functions and relation between logarithmic and inverse hyperbolic func

Graphs of Inverse hyperbolic functions and relation between logarithmic and inverse hyperbolic func

Graphs of Inverse hyperbolic functions and relation between logarithmic and inverse hyperbolic func

Laplace Transforms of f(t).t^n | Multiplication of t^n Concept with proof | Examples | Lecture-

Laplace Transforms of f(t).t^n | Multiplication of t^n Concept with proof | Examples | Lecture-

Graphs Of Inverse Hyperbolic Functions | Relation between logarithmic and inverse Hyperbolic Funct

Graphs Of Inverse Hyperbolic Functions | Relation between logarithmic and inverse Hyperbolic Funct

Initial Value Theorem and Final Value Theorems Laplace Transforms | Initial Value Example

Initial Value Theorem and Final Value Theorems Laplace Transforms | Initial Value Example

Laplace Transforms Of Derivatives Theorem | Laplace transforms of derivatives Examples |

Laplace Transforms Of Derivatives Theorem | Laplace transforms of derivatives Examples |

Inverse Hyperbolic Functions | Domain and Range of Inverse Hyperbolic Functions |Lecture - 3

Inverse Hyperbolic Functions | Domain and Range of Inverse Hyperbolic Functions |Lecture - 3

Second Shifting Theorem and Change Of Scale Properly of Laplace Transforms | Lecture-8

Second Shifting Theorem and Change Of Scale Properly of Laplace Transforms | Lecture-8

First Shifting Theorem Of Laplace Transforms | First Shifting Theorem and Examples | Lecture -7

First Shifting Theorem Of Laplace Transforms | First Shifting Theorem and Examples | Lecture -7

Derivative of Hyperbolic Functions | Examples | Lecture - 2

Derivative of Hyperbolic Functions | Examples | Lecture - 2

Unit step function of Laplace Transforms | Example of unit step Function | Lecture-6

Unit step function of Laplace Transforms | Example of unit step Function | Lecture-6

Laplace Transforms of L(cost^1/2 / t^1/2) | Examples | Lecture-5

Laplace Transforms of L(cost^1/2 / t^1/2) | Examples | Lecture-5

Examples Of Laplace Transforms | Lecture-4

Examples Of Laplace Transforms | Lecture-4

Hyperbolic Functions | Graphs, Domain and Range Of Hyperbolic Functions | Lecture- 1

Hyperbolic Functions | Graphs, Domain and Range Of Hyperbolic Functions | Lecture- 1

Maximum- Minimum Theorem of Continuous Function | Continuous Function | Lecture -

Maximum- Minimum Theorem of Continuous Function | Continuous Function | Lecture -

Laplace Transforms of Dirac Delta Function | Lecture-3

Laplace Transforms of Dirac Delta Function | Lecture-3

State and prove Intermediate Value Theorem | Continuous Function | Lecture

State and prove Intermediate Value Theorem | Continuous Function | Lecture

Laplace Transforms of Error Function and Unit Step Function | Lecture-2

Laplace Transforms of Error Function and Unit Step Function | Lecture-2

State and prove Bolzano Root Location Theorem | Continuous Function | Lecture - 7

State and prove Bolzano Root Location Theorem | Continuous Function | Lecture - 7

Piecewise Continuity, Function of Exponential Order, Definition and Existence of Laplace Transform

Piecewise Continuity, Function of Exponential Order, Definition and Existence of Laplace Transform

If f is continuous on [a,b] then f is bounded in [a,b] | Lecture 6

If f is continuous on [a,b] then f is bounded in [a,b] | Lecture 6

Important Theorem’s Of continuous Function On the closed interval | Lecture-5

Important Theorem’s Of continuous Function On the closed interval | Lecture-5

Indeterminate Forms 0^0, (infinity)^0 and 1^infinity | Lecture - 8

Indeterminate Forms 0^0, (infinity)^0 and 1^infinity | Lecture - 8

Indeterminate Form infinity - infinity | Lecture - 7

Indeterminate Form infinity - infinity | Lecture - 7

Indeterminate Form zero x infinity | Lecture - 6

Indeterminate Form zero x infinity | Lecture - 6

Indeterminate Form | L’ Hospital Rule for infinity / infinity | Lecture- 5

Indeterminate Form | L’ Hospital Rule for infinity / infinity | Lecture- 5

Indeterminate Forms | Examples of 0/0 form | Lecture-4

Indeterminate Forms | Examples of 0/0 form | Lecture-4

Indeterminate Forms | Examples of 0/0 form | Lecture-3

Indeterminate Forms | Examples of 0/0 form | Lecture-3

Indeterminate Forms | Examples of 0/0 form | Lecture-2

Indeterminate Forms | Examples of 0/0 form | Lecture-2

Indeterminate forms | L’Hospital Rule for 0/0 form | Examples | Lecture-1

Indeterminate forms | L’Hospital Rule for 0/0 form | Examples | Lecture-1

Infinite Limits | Definition and examples | Lecture- 13

Infinite Limits | Definition and examples | Lecture- 13

Connected Graphs, unilaterally Connected, Strongly and Weakly Connected Graphs | Lecture-9

Connected Graphs, unilaterally Connected, Strongly and Weakly Connected Graphs | Lecture-9

Graph Theory | Walks, Paths and Circuits | Lecture-8

Graph Theory | Walks, Paths and Circuits | Lecture-8

Infinite Limits | Prove (1+1/x)^x = e as x tends to infinity | Lecture- 12

Infinite Limits | Prove (1+1/x)^x = e as x tends to infinity | Lecture- 12

Infinite Limits | Definition and examples | Lecture-11

Infinite Limits | Definition and examples | Lecture-11

Graph Theory |Union and intersection of two graphs, Complement of a graph | Lecture-7

Graph Theory |Union and intersection of two graphs, Complement of a graph | Lecture-7

Between two distinct real numbers, there is always infinite many rational numbers | Lecture-24

Between two distinct real numbers, there is always infinite many rational numbers | Lecture-24

Between two distinct real numbers, there is always infinite many irrational numbers | Lecture-25

Between two distinct real numbers, there is always infinite many irrational numbers | Lecture-25

Graph Theory | Isomorphic Graphs, Homomorphic Graphs and Sub - graph | Lecture- 6

Graph Theory | Isomorphic Graphs, Homomorphic Graphs and Sub - graph | Lecture- 6

Graph Theory | Examples Of First Theorem on Graph Theory | Lecture-5

Graph Theory | Examples Of First Theorem on Graph Theory | Lecture-5

Prove that the set of natural Numbers is not bounded above | Lecture-24

Prove that the set of natural Numbers is not bounded above | Lecture-24

Graph Theory | Theorems on Graph Theory | Lecture- 4

Graph Theory | Theorems on Graph Theory | Lecture- 4

Properties Of Real Numbers | Archimedian Property | Lecture-23

Properties Of Real Numbers | Archimedian Property | Lecture-23

Non empty set of real numbers which is bounded below has greatest lower bound | Lecture-22

Non empty set of real numbers which is bounded below has greatest lower bound | Lecture-22

Graph Theory | First Theorem on Graph Theory ( Handshaking Theorem ) | Lecture- 3

Graph Theory | First Theorem on Graph Theory ( Handshaking Theorem ) | Lecture- 3

order of a graph, size of graph, in-degree and out-degree of vertex, source and sink, pendent vertex

order of a graph, size of graph, in-degree and out-degree of vertex, source and sink, pendent vertex

Non empty set of real numbers which is bounded above has least upper bound | Lecture-21

Non empty set of real numbers which is bounded above has least upper bound | Lecture-21

Graph Theory | What is Graph | Types Of Graph | Lecture-1

Graph Theory | What is Graph | Types Of Graph | Lecture-1

Ordered Completeness Property | Prove set of rational numbers is not order complete | Lecture - 20

Ordered Completeness Property | Prove set of rational numbers is not order complete | Lecture - 20

Sum of two bounded sets is Bounded Lecture- 19

Sum of two bounded sets is Bounded Lecture- 19

Properties of Real Numbers |Union of two bounded sets is bounded and conversely | Lecture-18

Properties of Real Numbers |Union of two bounded sets is bounded and conversely | Lecture-18

Properties Of Real Numbers | Examples Of l.u.b. Or Supremum and g.l.b. Or Infimum | Lecture- 17

Properties Of Real Numbers | Examples Of l.u.b. Or Supremum and g.l.b. Or Infimum | Lecture- 17

Properties Of Real Numbers | Examples Of l.u.b. Or Supremum and g.l.b. Or Infimum | Lecture- 16

Properties Of Real Numbers | Examples Of l.u.b. Or Supremum and g.l.b. Or Infimum | Lecture- 16

Properties Of Real Numbers | Greatest Lower Bound or Infimum | Lecture-15

Properties Of Real Numbers | Greatest Lower Bound or Infimum | Lecture-15

Properties Of Real Numbers | Least Upper Bound Or Supremum | Definition | Theorem | Lecture- 14

Properties Of Real Numbers | Least Upper Bound Or Supremum | Definition | Theorem | Lecture- 14

Properties Of Real Numbers | Bounded set, Bounded Above and Bounded Below | Lecture- 13

Properties Of Real Numbers | Bounded set, Bounded Above and Bounded Below | Lecture- 13

Properties Of Real Numbers- Examples Of Absolute Value or Numerical Value or Modulus | Lecture-12

Properties Of Real Numbers- Examples Of Absolute Value or Numerical Value or Modulus | Lecture-12

Properties Of Real Numbers- Examples Of Absolute Value or Numerical Value or Modulus | Lecture-11

Properties Of Real Numbers- Examples Of Absolute Value or Numerical Value or Modulus | Lecture-11

Properties Of Real Numbers | Examples Of Absolute Value Or Numerical Value Or Modulus | Lecture - 10

Properties Of Real Numbers | Examples Of Absolute Value Or Numerical Value Or Modulus | Lecture - 10

Properties Of Real Numbers | Examples Of Absolute Value Or Numerical Value Or Modulus | Lecture - 9

Properties Of Real Numbers | Examples Of Absolute Value Or Numerical Value Or Modulus | Lecture - 9

Properties Of Real Numbers | Absolute Value Or Numerical Value Or Modulus | Lecture - 8

Properties Of Real Numbers | Absolute Value Or Numerical Value Or Modulus | Lecture - 8

Prove that between two different rational numbers, there lie an infinite number of rational numbers

Prove that between two different rational numbers, there lie an infinite number of rational numbers

Properties Of Real Numbers | Examples | Prove 2^1/2 is irrational number | Lecture- 6

Properties Of Real Numbers | Examples | Prove 2^1/2 is irrational number | Lecture- 6

Properties Of Real Numbers | Ordered Field| Theorems | Lecture - 5

Properties Of Real Numbers | Ordered Field| Theorems | Lecture - 5

Properties Of Real Numbers | Order Axioms | Ordered Field | Lecture-4

Properties Of Real Numbers | Order Axioms | Ordered Field | Lecture-4

Properties Of Real Numbers | Theorems about Field Properties | Cancellation Law | Lecture-3

Properties Of Real Numbers | Theorems about Field Properties | Cancellation Law | Lecture-3

Properties Of Real Numbers | Theorems about Field Properties | Lecture-2

Properties Of Real Numbers | Theorems about Field Properties | Lecture-2

Properties Of Real Numbers | Algebraic Structure | Field Of Real Numbers | Lecture-1

Properties Of Real Numbers | Algebraic Structure | Field Of Real Numbers | Lecture-1

Mobius Inversion Formula | Example | Lecture-

Mobius Inversion Formula | Example | Lecture-

Mobius Inversion Formula | Examples | Lecture- 27

Mobius Inversion Formula | Examples | Lecture- 27

Mobius Inversion Formula | Examples | By using Möbius inversion formula find the value of phi(n)

Mobius Inversion Formula | Examples | By using Möbius inversion formula find the value of phi(n)

Converse Of Mobius Inversion Formula | Lecture- 25

Converse Of Mobius Inversion Formula | Lecture- 25

Mobius Inversion Formula | State and Prove Möbius inversion formula | Lecture - 24

Mobius Inversion Formula | State and Prove Möbius inversion formula | Lecture - 24

Mobius Function | Examples | If n is even integer, then prove summation mu(d) phi(d) = 0 where d|n

Mobius Function | Examples | If n is even integer, then prove summation mu(d) phi(d) = 0 where d|n

Mobius Function | Examples | Lecture - 22

Mobius Function | Examples | Lecture - 22

Mobius Function | E Merten’s Lemma | Theorem | Lecture- 21

Mobius Function | E Merten’s Lemma | Theorem | Lecture- 21

Mobius Function | Definition | Prove that Mobius function is multiplicative function | Lecture-20

Mobius Function | Definition | Prove that Mobius function is multiplicative function | Lecture-20

Perfect Number | Theorem | Examples | Every Even perfect number ends in 6 or 8 | Lecture- 19

Perfect Number | Theorem | Examples | Every Even perfect number ends in 6 or 8 | Lecture- 19

Sigma Function | Examples | If n is composite number then show sigma (n) is greater than n + n^1/2.

Sigma Function | Examples | If n is composite number then show sigma (n) is greater than n + n^1/2.

Sigma Function | Examples | Lecture-17

Sigma Function | Examples | Lecture-17

Sigma Function | Examples | Prove sigma ( 12 n - 1 ) is congruent to 0 (mod 12) | Lecture - 16

Sigma Function | Examples | Prove sigma ( 12 n - 1 ) is congruent to 0 (mod 12) | Lecture - 16

Sigma Function | Prove sigma (n) is odd iff n is a perfect square or twice a perfect square | Lec 15

Sigma Function | Prove sigma (n) is odd iff n is a perfect square or twice a perfect square | Lec 15

Sigma and Sigma k Functions | Theorems | Prove sigma function is multiplicative function |Lecture 14

Sigma and Sigma k Functions | Theorems | Prove sigma function is multiplicative function |Lecture 14

Divisor Function | Examples | Find the smallest value of n s.t. d(n) = 10 | Lecture- 13

Divisor Function | Examples | Find the smallest value of n s.t. d(n) = 10 | Lecture- 13

Divisor Function | Prove that divisor function d(n) is an odd integer iff n is perfect square |

Divisor Function | Prove that divisor function d(n) is an odd integer iff n is perfect square |

Divisor Function d(n) | Prove that divisor function d(n) is multiplicative function | Lecture - 11

Divisor Function d(n) | Prove that divisor function d(n) is multiplicative function | Lecture - 11

Euler’s Phi Function | Examples Of Gauss’s Theorem | Lecture- 10

Euler’s Phi Function | Examples Of Gauss’s Theorem | Lecture- 10

Euler’s Phi Function | Examples | For positive integer n, prove 1/2 is less than phi(n) | Lecture 9

Euler’s Phi Function | Examples | For positive integer n, prove 1/2 is less than phi(n) | Lecture 9

Euler’s Phi Function | Examples | If n is a composite number then phi (n) = n-n^1/2 | Lecture-8

Euler’s Phi Function | Examples | If n is a composite number then phi (n) = n-n^1/2 | Lecture-8

Euler’s Phi Function | Theorem | Prove summation k = n phi (n)/2, where ( n, k) = 1 | Lecture - 7

Euler’s Phi Function | Theorem | Prove summation k = n phi (n)/2, where ( n, k) = 1 | Lecture - 7

Euler’s Phi Function | Example | Find all positive integer n for which phi ( n ) = 24 | Lecture - 6

Euler’s Phi Function | Example | Find all positive integer n for which phi ( n ) = 24 | Lecture - 6

Euler’s Phi Function | Examples | Find all solution of n for which phi (n) = 8 | Lecture-5

Euler’s Phi Function | Examples | Find all solution of n for which phi (n) = 8 | Lecture-5

Euler’s Phi Function | Examples | Show that phi (3n)= 3 phi(n) iff 3|n | Lecture- 4

Euler’s Phi Function | Examples | Show that phi (3n)= 3 phi(n) iff 3|n | Lecture- 4

Euler’s Phi Function | Theorems | Gauss Theorem | Lecture 3

Euler’s Phi Function | Theorems | Gauss Theorem | Lecture 3

Euler’s Phi Function| Prove that Euler’s Phi function is multiplicative function | Lecture - 2

Euler’s Phi Function| Prove that Euler’s Phi function is multiplicative function | Lecture - 2

Arithmetic Functions | Euler’s Phi Function | Definition | Theorems | Lecture- 1

Arithmetic Functions | Euler’s Phi Function | Definition | Theorems | Lecture- 1

Jacobi’s Symbol | Examples | Evaluate (21/221), (215/253), (5/567), (3422/5683) | Lecture-18

Jacobi’s Symbol | Examples | Evaluate (21/221), (215/253), (5/567), (3422/5683) | Lecture-18

The Riemann Stieltjes Integral | Examples | integration of [5-x] d(log[x]) on [1,5] | Lecture - 24

The Riemann Stieltjes Integral | Examples | integration of [5-x] d(log[x]) on [1,5] | Lecture - 24

Jacobi’s Symbol | State and prove Jacobi’s Reciprocity Law | Lecture-17

Jacobi’s Symbol | State and prove Jacobi’s Reciprocity Law | Lecture-17

Jacobi’s Symbol | If Q an odd integer then (i) (-1/Q)= (-1)^(Q-1)/2 (ii) (2/Q) = (-1)^(Q^2-1)/8

Jacobi’s Symbol | If Q an odd integer then (i) (-1/Q)= (-1)^(Q-1)/2 (ii) (2/Q) = (-1)^(Q^2-1)/8

Quadratic Residues | Jacobi’s Symbol | Definition | Properties | Lecture -15

Quadratic Residues | Jacobi’s Symbol | Definition | Properties | Lecture -15

The Riemann Stieltjes Integral | Examples | Lecture-23

The Riemann Stieltjes Integral | Examples | Lecture-23

Quadratic Reciprocity Law | Examples | Mersenne Number | Lecture-14

Quadratic Reciprocity Law | Examples | Mersenne Number | Lecture-14

The Riemann Stieltjes Integral | Examples | Lecture-22

The Riemann Stieltjes Integral | Examples | Lecture-22

The Riemann Stieltjes Integral | Examples of Step Function as Integrator | Lecture - 21

The Riemann Stieltjes Integral | Examples of Step Function as Integrator | Lecture - 21

Quadratic Reciprocity Law | Examples | Check x^2 + 6x - 50 is congruent to 0 (mod 79) | Lecture-13

Quadratic Reciprocity Law | Examples | Check x^2 + 6x - 50 is congruent to 0 (mod 79) | Lecture-13

Quadratic Reciprocity Law | Find all primes such that (10/p) = 1 | Lecture - 12

Quadratic Reciprocity Law | Find all primes such that (10/p) = 1 | Lecture - 12

Quadratic Residues | Examples | List of all quadratic residue of 11 |Lecture-11

Quadratic Residues | Examples | List of all quadratic residue of 11 |Lecture-11

The Riemann Stieltjes Integral | Examples | Lecture-20

The Riemann Stieltjes Integral | Examples | Lecture-20

State and prove Quadratic Reciprocity Law | Lecture-10

State and prove Quadratic Reciprocity Law | Lecture-10

The Riemann- Stieltjes Integral | Examples | Lecture- 19

The Riemann- Stieltjes Integral | Examples | Lecture- 19

Quadratic Residues | If p is odd prime, then (2/p)= (-1)^(p^2-1)/8 | Lecture- 9

Quadratic Residues | If p is odd prime, then (2/p)= (-1)^(p^2-1)/8 | Lecture- 9

Quadratic Residues |Eisenstein’s Lemma | Lecture-8

Quadratic Residues |Eisenstein’s Lemma | Lecture-8

The Riemann Stieltjes Integral | Example | f(x) = x, alpha(x) = x+[x] | By Definition |Lecture-18

The Riemann Stieltjes Integral | Example | f(x) = x, alpha(x) = x+[x] | By Definition |Lecture-18

Quadratic Residue | Gauss Lemma | Lecture- 7

Quadratic Residue | Gauss Lemma | Lecture- 7

Quadratic Residues | Legendre Symbol | Examples | Lecture - 6

Quadratic Residues | Legendre Symbol | Examples | Lecture - 6

Quadratic Residues | Legendre Symbol | Definition | Properties | Lecture-5

Quadratic Residues | Legendre Symbol | Definition | Properties | Lecture-5

Quadratic Residue | p is greater than 3, prove sum of the quadratic residue is divisible by p

Quadratic Residue | p is greater than 3, prove sum of the quadratic residue is divisible by p

Quadratic Residues | Examples | Lecture-3

Quadratic Residues | Examples | Lecture-3

Quadratic Residues | Euler’s Criterion | Example | Lecture- 2

Quadratic Residues | Euler’s Criterion | Example | Lecture- 2

Quadratic Residues | Definition | Theorem | Examples | Lecture - 1

Quadratic Residues | Definition | Theorem | Examples | Lecture - 1

Exponential Congruence | For what value of b 9^x is congruent to b (mod 13) solvable | Lecture- 22

Exponential Congruence | For what value of b 9^x is congruent to b (mod 13) solvable | Lecture- 22

Indices | Binomial Congruence | Solve 4x^9 is congruent to 7 (mod 13) | Lecture - 21

Indices | Binomial Congruence | Solve 4x^9 is congruent to 7 (mod 13) | Lecture - 21

Indices | Properties of index | Example | Lecture-20

Indices | Properties of index | Example | Lecture-20

Indices | Properties of Index | Lecture-19

Indices | Properties of Index | Lecture-19

Indices ( Index of a number) | Definition | Construct the index table of (mod 5) | Lecture-18

Indices ( Index of a number) | Definition | Construct the index table of (mod 5) | Lecture-18

Prove that there is no primitive roots of 2^k, k is greater than or equal to 3 | Lecture- 17

Prove that there is no primitive roots of 2^k, k is greater than or equal to 3 | Lecture- 17

Primitive Roots | Find all primitive roots of 25 and 50 | Lecture- 16

Primitive Roots | Find all primitive roots of 25 and 50 | Lecture- 16

Primitive Root| If p is an odd prime then 2p^k kas primitive root,k is natural number | Lecture - 15

Primitive Root| If p is an odd prime then 2p^k kas primitive root,k is natural number | Lecture - 15

Primitive Roots | Find all primitive roots of 3^4 | Lecture - 14

Primitive Roots | Find all primitive roots of 3^4 | Lecture - 14

Primitive Roots | Find all primitive roots of 3^3 | Lecture - 13

Primitive Roots | Find all primitive roots of 3^3 | Lecture - 13

Primitive Roots | If p is an odd prime, then p^k has a primitive root | Lecture - 12

Primitive Roots | If p is an odd prime, then p^k has a primitive root | Lecture - 12

Primitive Roots | Find all primitive roots of 5^2 | Lecture - 11

Primitive Roots | Find all primitive roots of 5^2 | Lecture - 11

Primitive Roots | Theorem | Example | Find all primitive roots of 3^2 | Lecture-10

Primitive Roots | Theorem | Example | Find all primitive roots of 3^2 | Lecture-10

Primitive Roots | Find all primitive roots of 13 | Find all primitive roots of 17 | Lecture- 9

Primitive Roots | Find all primitive roots of 13 | Find all primitive roots of 17 | Lecture- 9

Primitive Roots | Prove every prime number has primitive root | Lecture- 8

Primitive Roots | Prove every prime number has primitive root | Lecture- 8

Primitive Roots | Definition | Examples | Lecture - 7

Primitive Roots | Definition | Examples | Lecture - 7

Primitive Roots | Examples | Find O(2) (mod 385) | Find O(43) (mod 18) | Lecture - 6

Primitive Roots | Examples | Find O(2) (mod 385) | Find O(43) (mod 18) | Lecture - 6

Primitive Roots | Examples | Order of an element | Lecture- 5

Primitive Roots | Examples | Order of an element | Lecture- 5

Primitive roots | Order of an element | Theorems | Lecture-4

Primitive roots | Order of an element | Theorems | Lecture-4

Primitive roots | Theorems | Order of an element | Lecture - 3

Primitive roots | Theorems | Order of an element | Lecture - 3

Primitive Roots and Indices | If O(a)(mod n)=k then O(a^m)(mod n) =k/(m,k) | Lecture -2

Primitive Roots and Indices | If O(a)(mod n)=k then O(a^m)(mod n) =k/(m,k) | Lecture -2

Primitive Roots and Indices | Order of an element | Definition | Theorems | Examples | Lecture - 1

Primitive Roots and Indices | Order of an element | Definition | Theorems | Examples | Lecture - 1

x^2 is congruent to -1 (mod p) has a solution iff p=2 or p is congruent to 1 (mod 4) Lecture-10

x^2 is congruent to -1 (mod p) has a solution iff p=2 or p is congruent to 1 (mod 4) Lecture-10

Wilson’s Theorem | Examples | Show 4 x 29! + 5! is congruent to 0 ( mod 31) | Lecture-9

Wilson’s Theorem | Examples | Show 4 x 29! + 5! is congruent to 0 ( mod 31) | Lecture-9

Number Theory | State and prove Wilson’s Theorem | Lecture - 8

Number Theory | State and prove Wilson’s Theorem | Lecture - 8

Fermat’s Theorem | Prove a^5 and a leave the same remainder when divided by 15 | Lecture-7

Fermat’s Theorem | Prove a^5 and a leave the same remainder when divided by 15 | Lecture-7

Fermat’s Theorem | Show 8th power of any integer is the type 17k-1 or 17k or 17k-1| Lecture-6

Fermat’s Theorem | Show 8th power of any integer is the type 17k-1 or 17k or 17k-1| Lecture-6

Fermat’s Theorem | Examples | If (a,42)=1 then a^6 is congruent to 1 (mod 168)| Example -5

Fermat’s Theorem | Examples | If (a,42)=1 then a^6 is congruent to 1 (mod 168)| Example -5

Fermat’s Theorem | Prove that (2222)^5555 + (5555)^2222 is congruent to 0 (mod 7)| Lecture-4

Fermat’s Theorem | Prove that (2222)^5555 + (5555)^2222 is congruent to 0 (mod 7)| Lecture-4

Fermat’s Theorem | Show (1835)^1910 + (1986)^2061 is congruent to 0 (mod 7) | Example | Lecture-3

Fermat’s Theorem | Show (1835)^1910 + (1986)^2061 is congruent to 0 (mod 7) | Example | Lecture-3

Fermat Theorem | Example | The last digit in ordinary decimal representation of 3^400 | Lecture-2

Fermat Theorem | Example | The last digit in ordinary decimal representation of 3^400 | Lecture-2

State and prove Fermat’s Little Theorem | Lecture - 1.

State and prove Fermat’s Little Theorem | Lecture - 1.

Prove x congruent to 3 (mod 5) and x congruent to 5 (mod 7) have simultaneous solution ( mod 35)

Prove x congruent to 3 (mod 5) and x congruent to 5 (mod 7) have simultaneous solution ( mod 35)

ax+by congruent to r and cx+dy congruent to s (mod n) has unique solution (mod n) where (ad-bc,n)=1

ax+by congruent to r and cx+dy congruent to s (mod n) has unique solution (mod n) where (ad-bc,n)=1

Congruence | Find two mutually incongruent solution | Lecture-28

Congruence | Find two mutually incongruent solution | Lecture-28

Congruence | Find three consecutive integers each having square factor | Lecture - 27

Congruence | Find three consecutive integers each having square factor | Lecture - 27

Brahmagupta, 7th Century A.D. | Example | Congruence | Lecture-25

Brahmagupta, 7th Century A.D. | Example | Congruence | Lecture-25

Congruence | Ancient Chinese Problem | Example | Lecture-24

Congruence | Ancient Chinese Problem | Example | Lecture-24

State and Prove Chinese Remainder Theorem | Lecture- 24

State and Prove Chinese Remainder Theorem | Lecture- 24

Solve Linear Diophantine Equations By Using Linear Congruence | Lecture - 23

Solve Linear Diophantine Equations By Using Linear Congruence | Lecture - 23

Linear Congruences In Two Variables | Examples | Lecture- 22

Linear Congruences In Two Variables | Examples | Lecture- 22

Linear Congruence ax congruent to b (mod m) has exactly d incongruent solutions, (a,m)=d, d|b.

Linear Congruence ax congruent to b (mod m) has exactly d incongruent solutions, (a,m)=d, d|b.

Linear Congruence ax congruent to b (mod m) has a solution iff d|m where (a,m)=b | Lecture-20

Linear Congruence ax congruent to b (mod m) has a solution iff d|m where (a,m)=b | Lecture-20

Linear Congruences | Definition | Congruent and Incongruent Solution | Residue Class | Lecture - 19

Linear Congruences | Definition | Congruent and Incongruent Solution | Residue Class | Lecture - 19

Examples of Euler’s Fermat Theorem | what are the last two digits of 3^100 | Lecture- 18

Examples of Euler’s Fermat Theorem | what are the last two digits of 3^100 | Lecture- 18

State and prove Euler’s Fermat Theorem | Lecture-17

State and prove Euler’s Fermat Theorem | Lecture-17

Reduced Residue System | Definition | Theorems | Lecture - 16

Reduced Residue System | Definition | Theorems | Lecture - 16

Complete Residue System | Examples | Show { -27,-18,10,17,20,49} (mod 6) is CRS | Lecture-15

Complete Residue System | Examples | Show { -27,-18,10,17,20,49} (mod 6) is CRS | Lecture-15

Complete Residue System | Definition | Theorems | Lecture-14

Complete Residue System | Definition | Theorems | Lecture-14

Congruence | Examples | Find missing digit x s.t. 51840 X 273581 = 1418243x040 | Lecture-13

Congruence | Examples | Find missing digit x s.t. 51840 X 273581 = 1418243x040 | Lecture-13

Congruence | Example | Find the last three digits of the number 5^1965 | Lecture- 12

Congruence | Example | Find the last three digits of the number 5^1965 | Lecture- 12

Congruence | Find the last two digits of 9^9^9 | what is the last digit of 2^400 | Lecture- 11

Congruence | Find the last two digits of 9^9^9 | what is the last digit of 2^400 | Lecture- 11

Find the smallest integer a greater than 2 s.t. 2|a, 3|(a+1), 4|(a+2), 5|(a+3), 6|(a+4). Lecture-10

Find the smallest integer a greater than 2 s.t. 2|a, 3|(a+1), 4|(a+2), 5|(a+3), 6|(a+4). Lecture-10

Examples Of Congruence | Find Remainder When 4444^4444 is divided by 9 | Lecture-9

Examples Of Congruence | Find Remainder When 4444^4444 is divided by 9 | Lecture-9

Examples | An odd prime p is express as sum of two squares iff p is congruent to 1(mod4)| Lecture 8

Examples | An odd prime p is express as sum of two squares iff p is congruent to 1(mod4)| Lecture 8

Examples Of Congruence | For prime p greater than 5 either p^2-1 or p^2 +1 divisible by 10 | Lec-7

Examples Of Congruence | For prime p greater than 5 either p^2-1 or p^2 +1 divisible by 10 | Lec-7

An integer divisible by 11 iff difference between sum of digits at odd and even places. Lecture-6

An integer divisible by 11 iff difference between sum of digits at odd and even places. Lecture-6

An integer is divisible by 4 iff integer formed by its last two digits is divisible by 4. Lecture 5

An integer is divisible by 4 iff integer formed by its last two digits is divisible by 4. Lecture 5

Congruence | An integer is divisible by 3 iff its sum of digits is divisible by 3 | Lecture 4

Congruence | An integer is divisible by 3 iff its sum of digits is divisible by 3 | Lecture 4

Congruence | An integer is divisible by 2 iff unit digit is divisible by 2 | Lecture-3

Congruence | An integer is divisible by 2 iff unit digit is divisible by 2 | Lecture-3

Congruence | Properties Of Congruence | Lecture-2

Congruence | Properties Of Congruence | Lecture-2

Congruences | Definition | properties Of Congruence | Lecture-1

Congruences | Definition | properties Of Congruence | Lecture-1

Check whether the integer 271 is prime or composite number | Lecture-45

Check whether the integer 271 is prime or composite number | Lecture-45

For n is greater than 2, prove that n^1/n is irrational number | Lecture-44

For n is greater than 2, prove that n^1/n is irrational number | Lecture-44

Prime Number And Their Distribution | Prove that 2^1/2 is irrational number | Lecture-43

Prime Number And Their Distribution | Prove that 2^1/2 is irrational number | Lecture-43

If a+b is not equal to zero with (a,b) =1, p is odd prime then (a+b, a^p+b^p/a+b)=1 or p. Lecture 42

If a+b is not equal to zero with (a,b) =1, p is odd prime then (a+b, a^p+b^p/a+b)=1 or p. Lecture 42

If p is prime. If (a,p^2) = (b,p^2)=p then find the value (a^2,p^2) and (ab,p^4)| Lecture-42

If p is prime. If (a,p^2) = (b,p^2)=p then find the value (a^2,p^2) and (ab,p^4)| Lecture-42

Prime Number And Their Distribution | Examples | Find n for which ( n^4 +4 ) is prime | Lecture- 41

Prime Number And Their Distribution | Examples | Find n for which ( n^4 +4 ) is prime | Lecture- 41

Prime Numbers And Their Distribution |if 2^n -1 is prime then n is prime | Lecture-40

Prime Numbers And Their Distribution |if 2^n -1 is prime then n is prime | Lecture-40

If p,q are primes s.t. P-q=2, show that p^p + q^q is a composite number. Lecture-39

If p,q are primes s.t. P-q=2, show that p^p + q^q is a composite number. Lecture-39

State and prove fundamental theorem of arithmetic or unique factorisation theorem. Lecture-38

State and prove fundamental theorem of arithmetic or unique factorisation theorem. Lecture-38

Prime And Composite Numbers | Prove that the number of primes are infinite | Lecture-37

Prime And Composite Numbers | Prove that the number of primes are infinite | Lecture-37

Prime Numbers | If p is prime and p|ab then prove p|a or p|b. Lecture-36

Prime Numbers | If p is prime and p|ab then prove p|a or p|b. Lecture-36

Prime And Composite Numbers | Prove every integer n greater than 1 has a prime factor | Lecture-35

Prime And Composite Numbers | Prove every integer n greater than 1 has a prime factor | Lecture-35

Diophantine Equations| Find all positive solution, if any of the 200x + 325y=100 | Lecture-34

Diophantine Equations| Find all positive solution, if any of the 200x + 325y=100 | Lecture-34

Linear Diophantine Equations | if (a,b) = d then ax + by = c has a solution iff c | d.Lecture-33

Linear Diophantine Equations | if (a,b) = d then ax + by = c has a solution iff c | d.Lecture-33