Which of the integers cannot be formed with $x^2+y^5$ So, I was asked by my teacher in school to solve this problem it really had me stumped.The problem is as follows:Given that $x$ and $y$ are integers, which of the following cannot be expressed in the form $x^2+y^5$?
$1.)\ 59170$
$2.)\ 59012$
$3.)\ 59121$
$4.)\ 59149$
$5.)\ 59130$
Is it possible for an elegant solution and not tedious trial and error?

I have found 
$$59170=9^5+11^2$$
$$59012=8^5+162^2$$
$$59149=9^5+10^2$$
$$59130=9^5+9^2$$
and $59121$ can't be expressed in this form.
