Isotropic forms in field of p-adic numbers

Hi,

for which primes are the quadratic forms

and

isotropic over the field over -adic numbers ?

A abbreviated form for the two quadratic forms above is and .

Define .

I can use the fact that a regular quadratic form over a field is isotropic if and

.

[ denotes the Hilbert symbol and the discriminant of .]

Moreover, a regular quadratic form over a field is isotropic if and

or { and }.

means actually that the residue classes of and are not equal modulo .

Let's come to the first form:

, therefore .

Now I have to check for which primes

in .

But I don't know how to solve it.

Please can you help me?

Thanks!

Regards

Alexander

Re: Isotropic forms in field of p-adic numbers

Hello,

this problem is still unsolved.

If you have any hints or ideas, it would be great if you would answer.

Bye,

Alexander