Problem
NT-B1-M11-P003 Squares Modulo \(4\)
#3
★☆☆☆☆ Level 1 of 5
Which residues can a square of an integer have modulo \(4\)?
Check even and odd integers.
If \(n\) is even, then \(n^2\equiv0\pmod4\). If \(n\) is odd, then \(n\equiv1\) or \(3\pmod4\), and in both cases \(n^2\equiv1\pmod4\). Only \(0\) and \(1\) are possible.
Will be used in impossibility arguments.