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The p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems
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$2$-adic valuation on $\mathbb Q (\sqrt{-15})$
I was reading the book "The structure of groups of prime power order". In the book (page 226, Example 10.1.18) it is proved that
$-15$ has a square root is $\mathbb Z_2$ where $\mathbb Z_2$ denotes th …