101 numbers in a line
Source: Argentina MO 2008
November 19, 2008
pigeonhole principlemodular arithmeticnumber theory unsolvednumber theory
Problem Statement
positive integers are written on a line. Prove that we can write signs \plus{}, signs and parenthesis between them, without changing the order of the numbers, in such a way that the resulting expression makes sense and the result is divisible by .