I was solving this question http://www.spoj.com/problems/HS08PAUL/, which asks number of integers in range $[1,n]$ which are expressible in form $x^2+y^4$, $x$ and $y$ being integers.
A simple implementive solution passes (loop $x$ for $1\leq x\leq\sqrt{n}$ and then $y$ till $x^2+y^4\leq n$, but I was wondering if there is some mathematical theorem governing such numbers.
More specifically: given an integer $n$, do there exist integers $x$ and $y$ such that $x^2+y^4=n$?