The list of topics a number theory book has to cover:
Divisibility
Remainders and Modular Arithmetic
Fundamental Theory of Arithmetic
Primes
Euclidean Algorithm
Residues

Quadratic Residues
Euler's Totient Function
Fermat's Little theorem
Bounding and Squeezing
Chinese Remainder Theorem
Multiplicative Inverse
Greatest Common Denominator
Least Common Multiple



The two books I mentioned were:
- "Olympiad Number Theory Through Challenging Problems" by Justin Stevens
- "104 Number Theory Problems" by Titu Andreescu, Dorin Andrica, Zuming Feng

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