Knowrap-adic valuationLinked fromLinked fromThe 8 pages that link to p-adic valuation, each with the reason it gives.All 8Broader topic 1Related 5Narrower topic 2DivisibilityBroader topic: Comparing prime valuations characterizes divisibility between nonzero integers.p-adic numberRelated: It determines p-adic absolute value and measures divisibility by p.Sylow theoremsRelated: It gives the exponent in the order of a Sylow p-subgroup.Hensel's lemmaRelated: Valuation measures how accurately each lifted approximation satisfies the polynomial equation.Legendre's formulaNarrower topic: The formula is an explicit valuation formula specialized to factorials.Lifting-the-exponent lemmaNarrower topic: The lemma’s output is precisely a prime-adic valuation.Ostrowski's theoremRelated: Its exponent data determine the absolute values in the non-Archimedean classes.Wolstenholme's theoremRelated: Valuations express the theorem as a lower bound on the prime-power divisibility of a difference.