Understand the problem Find all real numbers for which there exists a non-constant function satisfying the following two equations for all i) andii) Source of the problem Baltic Way 2016 Topic Functional Equations Difficulty Level Easy Suggested Book Functional...

Understand the problem We are given sets of size each. The size of the intersection of any two sets is exactly . Prove that all the sets have a common element. Source of the problem Austrian-polish mathematical Olympiad 1978 Topic Combinatorics Difficulty Level Easy...

Understand the problem Let be the set of positive integers. Determine all functions such that is divisible by for all positive integers . Source of the problem APMO 2019 Topic Number Theory Difficulty Level Medium Suggested Book An Excursion in Mathematics Start...

Understand the problem Each lottery ticket has a 9-digit number, which uses only the digits 1, 2, 3. Each ticket is coloured red, blue or green. If two tickets have numbers which differ in all nine places, then the tickets have different colours. Ticket 122222222 is...

Understand the problem Find all pairs of positive integers so that . Source of the problem Singapore MO 2008 Topic Number Theory Difficulty Level Medium Suggested Book An Excursion in Mathematics Start with hints Hint 0Hint 1Hint 2Hint 3Hint 4 Do you really need a...