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5

Part of 2011 Canada National Olympiad

Problems(1)

Canadian Mathematical Olympiad - 2011 - Question 5

Source:

4/6/2011
Let dd be a positive integer. Show that for every integer SS, there exists an integer n>0n>0 and a sequence of nn integers ϵ1,ϵ2,...,ϵn\epsilon_1, \epsilon_2,..., \epsilon_n, where ϵi=±1\epsilon_i = \pm 1 (not necessarily dependent on each other) for all integers 1≤i≤n1\le i\le n, such that S=∑i=1nϵi(1+id)2S=\sum_{i=1}^{n}{\epsilon_i(1+id)^2}.
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