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

Source: 1974 Swedish Mathematical Competition p6

March 26, 2021
number theoryPerfect SquareSum of Squares

Problem Statement

For which nn can we find positive integers a1,a2,…,ana_1,a_2,\dots,a_n such that a12+a22+⋯+an2 a_1^2+a_2^2+\cdots+a_n^2 is a square?
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