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)