Can one find 4004 positive integers such that the sum ...
Source: Balkan Math Olympiad BMO 2003, problem 1
October 24, 2005
pigeonhole principlealgebrapolynomialinductionnumber theorygreatest common divisor
Problem Statement
Can one find 4004 positive integers such that the sum of any 2003 of them is not divisible by 2003?