Number Theory Problems in Mathematical Competitions

by Amir Hossein Parvardi

This problem set was released for free public use as a thank you to all the people who supported the book Topics in Number an Olympiad-Oriented Approach, authored by Masum Billal and Amir Hossein Parvardi. You can download the PDF version from our book's website. 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. The problems have been classified into 7 conventional divisibility questions, modular arithmetic and congruence equations, and finding the remainder upon division by a specific number. Diophantine equations involving primes, reciprocals of numbers, factorials, and binomial coefficients. Arithmetic number of divisors, sum of divisors, functions from naturals to naturals, sum of digits, and Euler's totient function problems related to divisibility, finding the roots, and finding all polynomials with certain properties decimal system and decimal representation of numbers, binary representation, sum of digits, and finding numbers with specific conditions on their digits problems about integer, natural, or rational sequences, finding a specific term in the sequence, divisibility issues, and weird sums on sequence terms problems that do not fit in the above classes.

84 pages, Kindle Edition

Published May 10, 2018