1

Part of 2003 Balkan MO

Problems(1)

Can one find 4004 positive integers such that the sum ...

Source: Balkan Math Olympiad BMO 2003, problem 1

Can one find 4004 positive integers such that the sum of any 2003 of them is not divisible by 2003?

pigeonhole principlealgebrapolynomialinductionnumber theorygreatest common divisor