Definition talk:P-adic Valuation/Integers

Further thoughts on this.

Since, in the "also known as", it is stated that this is "usually" defined on the rationals, it make sense to make that one the main page. Then the merge with Definition:Multiplicity of Prime Factor, which can be defined as the restriction of this to the integers, can be implemented as a second definition on that page, rather than this one. --prime mover (talk) 02:01, 25 August 2017 (EDT)

Merge with Definition:Prime Decomposition/Multiplicity
Regarding the suggestion of a merge Definition:Prime Decomposition/Multiplicity it should be noted that the multiplicity of $p$ is only defined if $p$ is a prime factor of an integer, where as the $p$-adic valuation is always defined for every integer. The multiplicity of $p$ is never 0, but the $p$-adic valuation can be. This subtle difference means that the two definitions are not the same. --Leigh.Samphier (talk) 12:52, 7 April 2021 (UTC)