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