Number Theory Problems in Mathematical Competitions (2015 – 2016)

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Create Date November 26, 2018
Last Updated November 26, 2018

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.

Buy Kindle version from Amazon

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.

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  1. Thanks very nice blog!

  2. At the core of who you are you have the answer; you understand who you are and you know what you must do.

  3. Leopoldo Scerpella

    October 12, 2019 — 9:33 pm

    Thanks you! Excellent!

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