Question 30
Let $m \lt n$ be positive integers and $p = \frac{n^2 + m^2}{\sqrt{n^2 - m^2}}$.
a. Find three pairs of positive integers $(m, n)$ for which $p$ is a prime number.
b. Show that if $p$ is a prime number, then $p \equiv 1 \pmod 8$.
a. Find three pairs of positive integers $(m, n)$ for which $p$ is a prime number.
b. Show that if $p$ is a prime number, then $p \equiv 1 \pmod 8$.