Let $p$ be a prime number $(p \neq 2$ and $p \neq5)$, and let $A$ be some given number.
Suppose that $p$ divides the number $A^2 - 5$. Show that $p$ must be congruent to either 1 or 4 modulo 5.
A little confused about this number theory question. Any Help? I would love to see a solution to this problem. Thanks.
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