How to prove $x^2=-1$ has a solution in $\mathbb{Q}_p$ iff $p=1\mod 4$ Let $p$ be prime and let $\mathbb{Q}_p$ denote the field of $p$-adic numbers.
Is there an elementary way to prove $x^2=-1$ has a solution in $\mathbb{Q}_p$ iff $p=1\mod 4$?
I need this result, but I cannot find a reference. Can some recommend a good book or a set of (easily available) lecture notes to help me out? 

Following Euler Criterion 
http://en.wikipedia.org/wiki/Euler%27s_criterion
$-1$ is a quadratic residue if $(-1)^{\frac{(p-1)}2}=1$
which happens only when $\frac{(p-1)}2$ is even 
so $p-1$ is divisible by 4 
so $p\equiv1 (mod4)$
the book i would follow for number theory is Introduction to number theory by Hua Loo Keng 
this is a fairly comprehensive book can a bit a too much for elementary course so depending on your syllabus you may want to use an elementary text like Elementary number theory by Rosen.
