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happy naturals , a^2+b^2 = n, sum of perfect squares

Source: Norwegian Mathematical Olympiad 1997 - Abel Competition p1

February 11, 2020
Perfect SquareSumnumber theory

Problem Statement

We call a positive integer nn happy if there exist integers a,ba,b such that a2+b2=na^2+b^2 = n. If tt is happy, show that (a) 2t2t is happy, (b) 3t3t is not happy
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