<s>[INST] Perfect square is $0$ or $1$ modulo $4$ . Prove that for every integer $n$ either 


*

*$n^2 \equiv 0\pmod{4}$ or 

*$n^2\equiv 1\pmod{4}$
 [/INST] $n$ can be even or odd.
When $n=2k$ we get
$(2k)^2=4k^2 \equiv 0 \pmod 4$.
When $n=2k+1$ we get
$n^2 = (2k+1)^2 = 4k^2 + 4k + 1 \equiv 1 \pmod 4$.
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