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a_1^2+a_2^2+...+a_n^2 a perfect square

Source: 1999 Spanish Mathematical Olympiad P2

July 21, 2018
number theoryPerfect SquareInteger sequence

Problem Statement

Prove that there exists a sequence of positive integers a1,a2,a3,...a_1,a_2,a_3, ... such that a12+a22+...+an2a_1^2+a_2^2+...+a_n^2 is a perfect square for all positive integers nn.
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