Update on July 23, 2018: I am releasing this problem set as a thank you to all the people who supported my new book Topics in Number Theory: an Olympiad-Oriented Approach, which I co-authored with Masum Billal. You can download two chapters of the book for free from the book’s website (the password is Riemann).
More info on the problem set: this is a question bank containing number theory problems chosen from mathematical competitions and olympiads around the world in the 2015-2016 school year. The book contains more than 300 problems with various levels of difficulty and suits any person who wants to study elementary number theory. To see a demo of this problem set, please visit this page.
The problems have been classified into 7 categories:
Divisibility: conventional divisibility questions, modular arithmetic and congruence equations, and finding the remainder upon division by a specific number.
Diophantine Equations: equations involving primes, reciprocals of numbers, factorials, and binomial coefficients.
Arithmetic Functions: number of divisors, sum of divisors, functions from naturals to naturals, sum of digits, and Euler’s totient function
Polynomials: problems related to divisibility, finding the roots, and finding all polynomials with certain properties
Digits: decimal system and decimal representation of numbers, binary representation, sum of digits, and finding numbers with specific conditions on their digits
Sequences: problems about integer, natural, or rational sequences, finding a specific term in the sequence, divisibility issues, and weird sums on sequence terms
Miscellaneous: problems that do not fit in the above classes.