P-adic number
In mathematics, 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. The extension is achieved by an alternative interpretation of the concept of "closeness" or absolute value. In particular, two p-adic numbers are considered to be close when their difference is divisible by a high power of p: the higher the power, the closer they are. This property enables p-adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory – including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles.
known for
...999...999910-adic2-adic integers3-adicAdic numberDyadic integersDyadic numberField of p-adic numbersL-adicL-adic integersL-adic numberP-addic numberP-adicP-adic Division AlgorithmP-adic NumberP-adic digitP-adic division algorithmP-adic fieldP-adic groupP-adic groupsP-adic integerP-adic integersP-adic methodsP-adic metricP-adic numbersP-adicsP-nessRing of p-adic integers
Wikipage redirect
...999...99990.999...10-adic1 + 1 + 1 + 1 + ⋯1 + 2 + 4 + 8 + ⋯1 − 2 + 4 − 8 + ⋯2-adic integers3-adicAbelian groupAbraham FraenkelAbsolute Galois groupAbsolute value (algebra)Adams spectral sequenceAdic numberAhmed AbbesAlgebraic geometryAlgebraic number fieldAlgebraically compact moduleAnatoly KaratsubaAndrei ZelevinskyArchimedean groupArchimedean propertyAreas of mathematicsArithmetic dynamicsArithmetic geometryArityArtin conductorArtin–Hasse exponentialAutomorphic formAutomorphic numberAx–Kochen theoremAzumaya algebraBaker's theoremBanach algebraBasic Number TheoryBaum–Connes conjectureBerkovich spaceBernoulli numberBijective numeration
Link from a Wikipage to another Wikipage
known for
primaryTopic
P-adic number
In mathematics, 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. The extension is achieved by an alternative interpretation of the concept of "closeness" or absolute value. In particular, two p-adic numbers are considered to be close when their difference is divisible by a high power of p: the higher the power, the closer they are. This property enables p-adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory – including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles.
has abstract
Dalam matematika, Bilangan p-a ...... ilitas sistem bilangan adik p.
@in
El sistema de nombres p-àdics ...... ica modular d'aquestes corbes.
@ca
Em matemática, o sistema dos n ...... úmeros é na teoria de números.
@pt
En mathématiques, et plus part ...... l'on appelle analyse p-adique.
@fr
Für jede Primzahl bilden die p ...... s analog zur reellen Analysis.
@de
Il sistema dei numeri -adici è ...... tica modulare di queste curve.
@it
In de getaltheorie, een deelge ...... e vorm van wiskundige analyse.
@nl
In mathematics, the p-adic num ...... rds such as dyadic or triadic.
@en
Inom matematiken är de p-adisk ...... exempel de "i-adiska talen").
@sv
P-adická čísla (značená Qp) js ...... ropojování algebry s analýzou.
@cs
Link from a Wikipage to an external page
Wikipage page ID
page length (characters) of wiki page
Wikipage revision ID
1,025,915,135
Link from a Wikipage to another Wikipage
title
p-adic Number
@en
urlname
p-adicNumber
@en
wikiPageUsesTemplate
type
comment
Dalam matematika, Bilangan p-a ...... khir Fermat oleh Andrew Wiles.
@in
El sistema de nombres p-àdics ...... camp de la teoria de nombres.
@ca
Em matemática, o sistema dos n ...... úmeros é na teoria de números.
@pt
En mathématiques, et plus part ...... ommée valeur absolue p-adique.
@fr
Für jede Primzahl bilden die p ...... s analog zur reellen Analysis.
@de
Il sistema dei numeri -adici è ...... tica modulare di queste curve.
@it
In de getaltheorie, een deelge ...... grijke rol in de getaltheorie.
@nl
In mathematics, the p-adic num ...... Last Theorem by Andrew Wiles.
@en
Inom matematiken är de p-adisk ...... analys för de p-adiska talen.
@sv
P-adická čísla (značená Qp) js ...... cká čísla, 5-adická čísla atp.
@cs
label
Bilangan p-adik
@in
Liczby p-adyczne
@pl
Nombre p-adique
@fr
Nombre p-àdic
@ca
Numero p-adico
@it
Número p-ádico
@es
Número p-ádico
@pt
P-adic number
@en
P-adické číslo
@cs
P-adisch getal
@nl