What do you mean by no trivial solution in ?
In we have solutions for all .
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!
Sorry that was a typo! Thats meant to be in Q.
this equation has nontrivial solutions overQp for all prime numbers p and over R but has no nontrivial solutions over Q.
I need to show that although there is no solution in Q there is a solution in Qp . But I don`t know how to show that for the case where modulo p=2 and modilo p=17?
Its a special case, but its completely confused me.
Thanks so much for the reply!