In the field of rationals [itex]\mathbb{Z}_{(p)}[/itex] (rationals in the ring of the p-adic integers), how is it possible to prove the residue field [itex]\mathbb{Z}_{(p)}/p\mathbb{Z}_{(p)}[/itex] is equal to [itex]\mathbb{Z}/p\mathbb{Z}[/itex] ?(adsbygoogle = window.adsbygoogle || []).push({});

I've narrowed it down to [itex]\mathbb{Z}_{(p)}/p\mathbb{Z}_{(p)} = \left\{ a/b\in\mathbb{Q} : p\nmid a, p \nmid b \right\} [/itex], but can't seem to make the last step...

Or maybe I'm barking up the wrong tree. Hmm...

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# Residue field of p-adic integers

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