Given pairwise coprime natural numbers $ x $, $ y $, $ z $, $ t $ such that $ 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.
Source: 239 2000 J2
Tags: number theory
Given pairwise coprime natural numbers $ x $, $ y $, $ z $, $ t $ such that $ 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.