How to prepare for Number Theory at Math Competitions and the International Math Olympiad

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