Help!

Show that = - 17 has no integer solutions.

(Hint: Show using quadratic reciprocity that y is a square mod 17 by considering each prime

divisor of y. Use this to show 2 is a fourth power mod 17, a contradication.)

Using the fundamental theorem of arithmetic, i assume

By Euler's Criterion (y/17) (mod 17)

I get if any of the exponents are even, then

If any of the exponents are odd, then

This is where i get stuck. (Sorry about the bad notation, i haven't quite figured out LaTeX)