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$ xy + yz + zt = xt $ then the sum of squares of some two

Source: 239 2000 J2

May 17, 2020
number theory

Problem Statement

Given pairwise coprime natural numbers x x , y y , z z , t t such that xy+yz+zt=xt xy + yz + zt = xt . Prove that the sum of the squares of some two of these numbers is twice the sum of the squares of the two remaining.
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