Question 1033733
If x and y are supposed to be natural numbers such that xy = 8, then the only ordered pairs (x,y) possible are (1,8), (2,4), (4,2), and (8,1).

By direct substitution, (1,8), (2,4), and (8,1) will not satisfy {{{x^3 + 4 = 17y^2}}}.  (Use you calculator to confirm!)  The only pair that satisfies is (4,2).