Problem
ALG-B1-M11-P015 Modular obstruction
#15
★★★☆☆ Level 3 of 5
Prove that \(x^2+y^2=4k+3\) is impossible in integers.
Work modulo \(4\).
Squares modulo \(4\) are \(0\) or \(1\). A sum of two squares cannot have residue \(3\).
Strategy: quick obstruction instead of search.