How to prove that for any natural no m Pythagorean templates can be expressed in2m,m+1,m-1

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How to prove that the square of an odd integer can express in the form of (8m+1), for some positive integer m?

(w i t h n \geq m)

(\begin{matrix} n m \end{matrix}) =^{n} C_{m}

(\begin{matrix} n m \end{matrix}) + (\begin{matrix} n - 1 m \end{matrix}) + (\begin{matrix} n - 2 m \end{matrix}) + . . . . . . . . . . + (\begin{matrix} m m \end{matrix}) = (\begin{matrix} n + 1 m + 1 \end{matrix})

m

n + 1, n + 2, \dots, n + m

\frac{\sqrt{(1 + m)} + i \sqrt{(1 - m)}}{\sqrt{(1 + m)} - i \sqrt{(1 - m)}} - \frac{\sqrt{(1 - m)} + i \sqrt{(1 + m)}}{\sqrt{(1 - m)} - i \sqrt{(1 + m)}} (m \in R)

If a natural number 'm' can be expressed as $n^{2}$ , then 'm' is a _____ number.

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