Chapter 0.2, Problem 34E

(a)

To determine

Toprove: That $m$ is the sum of the squares of two integers where $m$ and $n$ are integers such that $n^2+1=2m$.

(b)

To determine

$9,561,565$ as the sum of two squares when it is given that ${\left(4373\right)}^2+1=2\left(9,561,565\right)$.