I'm trying to find *every* [discrete valuation](http://en.wikipedia.org/wiki/Discrete_valuation) on the field of rational numbers.

If $a\in \mathbb Q$, we can write $a=p^j\frac{x}{y}$, where $p$ is a prime number and $p\nmid x$ and $p\nmid y$. We can define the p-adic valuation $v\_p(a)=j$.

I found easy to prove this is indeed a discrete valuation. I would like to know if there is another discrete valuation over the rational numbers and if the answer is yes, how many? why?

I need help

Thanks in advance