Linked from

The 15 pages that link to p-adic number, each with the reason it gives.

• Real numberCompared with: The p-adic numbers complete the rationals using a distance unlike ordinary real distance.

• Rational numberCompared with: The rational numbers also serve as the starting field for p-adic completions.

• Modular arithmeticCompared with: P-adic arithmetic organizes integers by congruences modulo increasingly high powers of a prime.

• Cauchy sequenceRelated: Cauchy sequences under the p-adic distance build this distinct number system.

• p-adic valuationBroader topic: Completing with the distance derived from this valuation produces the p-adic numbers.

• Algebraic number fieldBroader topic: Completing a number field at a prime yields a local arithmetic perspective.

• Helmut HasseRelated: These numbers provide the local settings central to Hasse’s arithmetic methods.

• Local-global principleRelated: Each prime gives a nonarchimedean local field in which equations can be tested.

• Arithmetic geometryRelated: P-adic solutions capture behavior near a chosen prime.

• Hensel's lemmaRelated: Hensel developed the lemma as a tool for working with these number systems.

• Number (mathematics)Related: P-adic numbers support number-theoretic methods using a notion of distance unlike the real one.

• Birch's theoremRelated: Solubility over every p-adic field is part of the local conditions behind the main term.

• Leopoldt's conjectureRelated: Local units are formed in completions of the field at primes above p.

• Ostrowski's theoremRelated: Each prime-indexed class gives a corresponding p-adic completion.

• Wolstenholme's theoremRelated: The reciprocal-sum version is naturally interpreted through p-adic divisibility.