Problem
ALG-B1-M12-P032 Variant 8, Problem 4
#32
★★★★★ Level 5 of 5
Prove that \(x^2+y^2+z^2=8k+7\) has no integer solutions.
Squares modulo \(8\).
Squares give \(0,1,4\); the sum of three such residues is not \(7\).
Mock olympiad problem. Tags: modular-arithmetic.