Problem
NT-B1-M03-P002 Squares Modulo 4
#2
★☆☆☆☆ Level 1 of 5
Prove that the square of an integer modulo \(4\) can only have residue \(0\) or \(1\).
Check even and odd integers.
If \(n=2k\), then \(n^2=4k^2\equiv0\pmod4\). If \(n=2k+1\), then \(n^2=4k^2+4k+1\equiv1\pmod4\).
Basic table for impossibility arguments.