Problem
NT-B1-M06-P009 The Equation \(x^2=12y^2\)
#9
★★☆☆☆ Level 2 of 5
Prove that \(x^2=12y^2\) has no positive integer solutions.
First use the factor \(4\) on the right-hand side.
From \(x^2=12y^2\), \(x\) is even: \(x=2u\). Then \(4u^2=12y^2\), so \(u^2=3y^2\). But \(u^2=3y^2\) has no positive integer solutions by descent with prime \(3\). Contradiction.
Useful practice reducing the coefficient to a square factor and a prime.