Consider the following equation :
$4x^2+1=5^y~$ with $y>1$
Has this equation solutions in integers ?
I wrote small Maple program in order to find solutions but couldn't find anyone .
for x from 1 to 6000 do for y from 2 to 2000 do if 4*x^2+1 = 5^y then print(x,y); end if; end do; end do;