@TedShifrin @KajHansen @Hippalectryon @MikeMiller Heya!!! I want to check if the equation $3x^2+5y^2-7z^2=0$ has a solution in $\mathbb{Q}_2$.
Can I use the following theorem?
If $2 \nmid abc$ and $a+b \equiv 0 \pmod 4$, then the equation $ax^2+by^2+cz^2=0 $ has at least one non-trivial solution in $\mathbb{Q}_2$.
If so, is it like that?
$a+b=3+5 \equiv 8≡0 \pmod4 $ So, there is no solution in $\mathbb{Q}_2$.