We want to solve the linear Diophantine equation with 3 variables:
35x+55y+77z=1
for integer solutions in
Three methods are discussed:
1. Split the equation into two linear equation each of which has two variables.
2. Parameterize with canonical form
3. Particular solution and general solutions of homogeneous equations
Check out the videos on the GCD, Euclidean algorithms here
Two Basic Theorems on gcd (Greatest Common Divisors) of Two Integers (Bezout's Identity)
[ Ссылка ]
An Example of GCD, and Extended Euclidean Algorithm In Finding the Bezout Coefficients
[ Ссылка ]
GCD, Euclidean Algorithm and Bezout Coefficients
[ Ссылка ]
00:00 Introduction
00:21 Review of Equation with 2 Variables
02:24 Method 1: Split Into 2 Equations
06:00 Method 2: Parameterize with Canonical Form
13:30 Method 3: Particular solution and General solutions
