Let $p>2$ be prime and $m,n,r \in \mathbb{Z}^+$. Why is $$\frac{1}{2}(p^{rmn-r})(p^r - 3)$$ an odd number when $p \equiv_4 1$ or when $r$ is even?
I'm not really sure how to approach this.
2026-04-02 18:19:13.1775153953
Why is $\ \frac{1}{2}(p^{rmn-r})(p^r - 3)\ $ odd?
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