Problem
NT-B1-M03-P014 The Equation \(x^2=3y^2+2\)
#14
★★★☆☆ Level 3 of 5
Prove that \(x^2=3y^2+2\) has no integer solutions.
Consider the equation modulo \(3\).
The right side \(3y^2+2\equiv2\pmod3\). But a square modulo \(3\) is only \(0\) or \(1\). Thus the left side cannot have residue \(2\). Contradiction.
An example of choosing the modulus from the coefficient.