I was wondering if anyone could help me on this problem I am having.
I have the equation:
y^2 = 2( x^4 -17)
(which I am showing has no real solutions but has solutions in the p-adic numbers i.e. a counterexample to the hasse principle)
I need to show that it has a non trivial solution in R and in Q_p (p-adic numbers for p=2, 17 (the 2-adics and 17-adic)
Any help or advice would be so much apprciated! I`m completely stumped!