Primes of the form $x^2+ny^2$ where $n\equiv 1\pmod{4}$ is a squarefree number Let $n\equiv1\pmod{4}$ be a squarefree number and $p\equiv1\pmod{4n}$ be a prime number. Does there exist $x,y\in\mathbb{N}$ such that $p=x^2+ny^2$?
How about:  p=5, n=1, x=1, y=2
How about:  p=5, n=1, x=1, y=2