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Proof that the square of any positive in...

Proof that the square of any positive integer is of the form of `4m` or `4m+1` for some integer m.

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Euclid damma division theorem
a=2q,2q+1, where 2 is a whole number.
`a^2=(2q)^2=4q^2=4m`, where q is a whole number.
`a^2=(2q+1)^2=4q^2+4q+1=4m+1` where `m=(q^2+q)`.
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