Prove that for $\displaystyle \forall x \in \mathbb{Q}_p, x =\pm \prod_{p<\infty} p^{\nu_p (x)}$, where the positive sign is selected if x is a square at infinity.

Any help would be greatly appreciated.

Thanks,

Arlington

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- Jan 8th 2012, 03:10 PMarlingtonbassettp-adic valuation question
Prove that for $\displaystyle \forall x \in \mathbb{Q}_p, x =\pm \prod_{p<\infty} p^{\nu_p (x)}$, where the positive sign is selected if x is a square at infinity.

Any help would be greatly appreciated.

Thanks,

Arlington