Problem
NT-B1-M06-P008 The Equation \(x^2=8y^2\)
#8
★★☆☆☆ Level 2 of 5
Prove that \(x^2=8y^2\) has no positive integer solutions.
First show that \(x\) is even, and reduce the equation.
From \(x^2=8y^2\), \(x\) is even. Let \(x=2u\). Then \(4u^2=8y^2\), so \(u^2=2y^2\). But this equation has no positive integer solutions. Hence the original equation has none.
This is not a new descent, but a reduction to the basic one.