Problem
ALG-B1-M12-P025 Variant 7, Problem 1
#25
★★★★★ Level 5 of 5
Prove that \(x^2+y^2=8xy\) has no positive integer solutions.
Vieta descent.
For a minimal solution \(x>y\). The other root \(x'=8y-x=\frac{y^2}{x}\) is positive, integral, and smaller than \(y\). Contradiction.
Mock olympiad problem. Tags: vieta-jumping.