17 Feb 09
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.