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Posers and Puzzles

Posers and Puzzles

  1. 17 Feb '09 10:37
    Consider the integers a_1, a_2, ... a_n, n >= 3.
    Show that there exists an integer k such that for all 1 <= i,j <= n
    a_i+a_j+k is not divisible by N, where N=n*(n+1)/2

    I've found a solution, but i feel it was unmotivated so i'm wondering if anyone can find a more natural way of going about it.