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Sequence

Source: Chinese TST 2007 2nd quiz P2

January 3, 2009
modular arithmeticalgebra proposedalgebra

Problem Statement

Find all positive integers n n such that there exists sequence consisting of 1 1 and −1:a1,a2,⋯ ,an - 1: a_{1},a_{2},\cdots,a_{n} satisfying a1⋅12+a2⋅22+⋯+an⋅n2=0. a_{1}\cdot1^2 + a_{2}\cdot2^2 + \cdots + a_{n}\cdot n^2 = 0.
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