Prove that a perfect square is either a multiple of $4$ or of the form $4q+1$ for some $q\in \mathbb{Z}$.
Any ideas on how to start? Do I use a proof by contraposition? Also what's the definition of a perfect square?
[Math] Prove that a perfect square is either a multiple of $4$ or of the form $4q+1$.
discrete mathematics
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Best Answer
Hint: A perfect square is an integer $k$ such that $k = n^2$ for some integer $n$. It follows that $k$ must be non-negative and that $n$ can be chosen to be non-negative. As for approaching the problem, first break it up into two cases: $k$ even and $k$ odd.