Problem
ALG-B1-M12-P017 Variant 5, Problem 1
#17
★★★★☆ Level 4 of 5
Prove that \(x^2+y^2=4k+3\) has no integer solutions.
Modulo \(4\).
Squares give \(0,1\); the sum cannot give \(3\).
Mock olympiad problem. Tags: modular-arithmetic.