MathDB
101 numbers in a line

Source: Argentina MO 2008

November 19, 2008
pigeonhole principlemodular arithmeticnumber theory unsolvednumber theory

Problem Statement

101 101 positive integers are written on a line. Prove that we can write signs \plus{}, signs × \times 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 16! 16!.