Proof Writing & Problem Solving · Easy problem

Someone claims: "if $n$ is odd, then $n^2 + 1$ is divisible by $4$." A direct computation with $n = 2k + 1$ gives $n^2 + 1 = 4k^2 + 4k + 2$, which settles the claim. What remainder does $n^2 + 1$ leave when divided by $4$, for every odd $n$?