Who was the first person to prove that only primes of the form $4k+1$ can evenly divide odd integers of the form $n^2+1$?

Question

I am writing a paper and I want to cite the person(s) who proved that only primes of the form $4k+1$ can evenly divide odd integers of the form $n^2+1$.

Edit: added "odd"

For example, if $n=8$, then $n^2 + 1 = 65$. Both 5 and 13 evenly divide 65 and both are prime numbers of the form $4k+1$.