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(8a-5b)^2 + (3b-2c)^2 + (3c-7a)^2 = 2

Source: 1998 Swedish Mathematical Competition p1

April 2, 2021
number theorydiophantineDiophantine equation

Problem Statement

Find all positive integers a,b,ca, b, c, such that (8a−5b)2+(3b−2c)2+(3c−7a)2=2(8a-5b)^2 + (3b-2c)^2 + (3c-7a)^2 = 2.
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