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Czech-Polish-Slovak Match 2016

Source: Czech-Polish-Slovak Match 2016,P2,day 2

July 12, 2016
number theory

Problem Statement

Prove that for every non-negative integer nn there exist integers x,y,zx, y, z with gcd(x,y,z)=1gcd(x, y, z) = 1, such that x2+y2+z2=32nx^2 + y^2 + z^2 = 3^{2^n}.(Poland)
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