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250 numbers are chosen in pos. integers not exceeding 501

Source: Tuymaada 2008, Junior League, Second Day, Problem 8.

July 20, 2008
number theoryprime numbersnumber theory unsolved

Problem Statement

250 numbers are chosen among positive integers not exceeding 501. Prove that for every integer t t there are four chosen numbers a1 a_1, a2 a_2, a3 a_3, a4 a_4, such that a_1 \plus{} a_2 \plus{} a_3 \plus{} a_4 \minus{} t is divisible by 23. Author: K. Kokhas
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