Infinitely Many Triples

★ 8/10Diophantine Equations number theory Vieta's Formulas

Problem

Prove that there are infinitely many triples of positive integers $x, y, z$ with

(x + y + z)^2 + 2(x + y + z) = 5(xy + yz + zx).

Answer

Solution

Difficulty	8/10
Topics	Diophantine Equations, number theory, Vieta's Formulas

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