Problem
NT-B2-M02-P004 A Square Plus One
#4
★★☆☆☆ Level 2 of 5
Find all residues \(n\pmod5\) such that \(5\mid n^2+1\).
Squares modulo \(5\) are \(0,1,4\).
We need \(n^2\equiv-1\equiv4\pmod5\). This occurs for \(n\equiv2\) or \(n\equiv3\pmod5\).
This introduces the language that \(-1\) is a square modulo a number.