What is P-adic number?
[[File:3-adic integers with dual colorings.svg|thumb|3-adic integers with dual colorings]] {{DISPLAYTITLE:''p''-adic number}} In [[mathematics]], '''{{mvar|p}}-adic numbers''' come from an alternate way of defining the [[distance]] between two [[rational number]]s.<ref>{{Citation|last=Gouvêa|first=Fernando Q.|title=p-adic Numbers|date=1997|url=https://doi.org/10.1007/978-3-642-59058-0_4|work=p-adic Numbers: An Introduction|series=Universitext |pages=43–85|editor-last=Gouvêa|editor-first=Fernando Q.|place=Berlin, Heidelberg|publisher=Springer|language=en|doi=10.1007/978-3-642-59058-0_4|isbn=978-3-642-59058-0|s2cid=118340827 |access-date=2022-05-04}}</ref><ref>{{Cite journal|last=Koblitz|first=Neal|date=1984|title=p-adic Numbers, p-adic Analysis, and Zeta-Functions|url=https://link.springer.com/book/10.1007/978-1-4612-1112-9|journal=Graduate Texts in Mathematics|volume=58 |language=en|doi=10.1007/978-1-4612-1112-9|isbn=978-1-4612-7014-0 |issn=0072-5285}}</ref> {{mvar|p}}-adic numbers are based in [[modular arithmetic]], which is a method of counting that loops back on itself, like a clock.<ref>{{Cite web|last=Houston-Edwards|first=Kelsey|date=2020-10-19|title=An Infinite Universe of Number Systems|url=https://www.quantamagazine.org/how-the-towering-p-adic-numbers-work-20201019/|access-date=2022-05-04|website=Quanta Magazine|language=en}}</ref> 2018 Fields Medalist [[Peter Scholze]] is an expert in this area.<ref>{{Cite web|last=Lamb|first=Evelyn|title=The Numbers behind a Fields Medalist's Math|url=https://blogs.scientificamerican.com/roots-of-unity/the-numbers-behind-a-fields-medalists-math/|access-date=2022-05-04|website=Scientific American Blog Network|language=en}}</ref> == History == The {{mvar|p}}-adic numbers were invented at the beginning of the twentieth century by the German [[mathematician]] Kurt Hensel. The aim was to make the methods of [[power series]] expansions, which play such a dominant role in the theory of [[Function (mathematics)|function]]s, available to the [[number theory|theory of numbers