On the Diophantine equation $2\sp n+px\sp 2=y\sp p$
On the Diophantine equation $2\sp n+px\sp 2=y\sp p$
Let p be a prime with $p > 3$. In this paper we prove that: (i) the equation ${2^n} + p{x^2} = {y^p}$ has no positive integer solution (x, y, n) with $\gcd (x,y) = 1$; (ii) if $p \nequiv 7 \pmod 8$, then the equation has no positive integer …