Problem
NT-B1-M03-P005 Square Equal to One
#5
★☆☆☆☆ Level 1 of 5
Find all residues \(n\pmod5\) for which \(n^2\equiv1\pmod5\).
Check residues \(0,1,2,3,4\).
Squares modulo \(5\): \(0^2\equiv0\), \(1^2\equiv1\), \(2^2\equiv4\), \(3^2\equiv4\), \(4^2\equiv1\). Thus \(n\equiv1\) and \(n\equiv4\pmod5\) work.
Important to speak about residues, not individual numbers.