MathDB

Canadian Mathematical Olympiad - 2011 - Question 5

Source:

April 6, 2011

number theory proposednumber theory

Problem Statement

Let

d

be a positive integer. Show that for every integer

S

, there exists an integer

n>0

and a sequence of

n

integers

\epsilon_1, \epsilon_2,..., \epsilon_n

, where

\epsilon_i = \pm 1

(not necessarily dependent on each other) for all integers

1\le i\le n

, such that

S=\sum_{i=1}^{n}{\epsilon_i(1+id)^2}