The second volume, Book 2, of Introduction to Number Theory in Mathematics Contests starts with focusing on the most important classical, basically polynomial congruences, and arithmetic functions. It features beautiful problems with unique and interesting results, such as the Erdös-Ginzburg-Ziv theorem (stating that among any \(2n - 1\) integers, one can find \(n\) whose sum is divisible by \(n\)), and also some other classical results arising from the Prime Number Theorem.

The important (because of its many applications) “lifting the exponent” lemma is present in the book as well along with the beautiful theorem of Lucas about binomial coefficients modulo a prime, Lagrange’s theorem on the number of solutions of a polynomial congruence modulo a prime, and Gauss’s theorem about the existence/non-existence of primitive roots modulo an arbitrary positive integer.