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

Source: Dutch MO 2008 p3

September 1, 2019
combinatoricsnumber theorydivisibledivides

Problem Statement

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.
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