arXiv:math/07037 67v2 [math.NT] 10 Nov 2007 Non-trivial solutions to a linear equation in integers Boris Bukh Abstract Fork≥3 letA⊂[1, N]beasetnot containinga solution to a 1 x 1 +***+ a k x k =a 1 x k+1 +***+a k x 2k indistinct integers.