TITLE: History of $p$-adic numbers
QUESTION [10 upvotes]: I'm interested in learning about the historical motivation and development of $p$-adic numbers. I haven't been able to find any books on the topic. I'd appreciate any references, including to more general history books which include coverage of the $p$-adics. Alternatively, if anyone has any knowledge about the history of $p$-adic numbers, feel free to post a summary here, particularly if you can highlight any names, papers and keywords that I could use to do more research on my own.
I'm not looking for a simplified overview, I want to really dig into the details, but any amount of information that could get me started is appreciated.

REPLY [8 votes]: One useful starting point is Peter Roquette's History of Valuation Theory. This may be a bit more general than you seek, but it has a bibliography that should provel helpful locating other sources. See also F. Gouvea, Hensel’s p-adic Numbers: early history, and the following
Ullrich, Peter, 1998: The genesis of Hensels p-adic numbers.
In the book:  $ $ P. L. Butzer, H.Th.
Jongen,W. Oberschelp (edd.), Charlemagne and his Heritage. 1200 Years of
Civilization and Science in Europe. / Karl der Große und sein Nachwirken.
1200 Jahre Kultur und Wissenschaft in Europa. Vol. 2. Mathematical Arts.
Thurnhout: Brepols, 163-178