Problem
NT-B2-M02-P002 A Sum of Two Squares
#2
★★☆☆☆ Level 2 of 5
Prove that \(x^2+y^2=4z+3\) has no integer solutions.
Look at the equation modulo \(4\).
A square modulo \(4\) is \(0\) or \(1\). Hence a sum of two squares modulo \(4\) can be only \(0,1,2\). The right-hand side has residue \(3\), contradiction.
A classic short problem on choosing the right small modulus.