MathDB

3

Part of 2008 Dutch Mathematical Olympiad

Problems(1)

set S 756 of arbitrary integers between 1 and 2008 , exist a,b in S=> 8 \ (a+b)

Source: Dutch MO 2008 p3

9/1/2019
Suppose that we have a set SS of 756756 arbitrary integers between 11 and 20082008 (11 and 20082008 included). Prove that there are two distinct integers aa and bb in SS such that their sum a+ba + b is divisible by 88.
combinatoricsnumber theorydivisibledivides