P-adic order

P-adic order

In number theory, for a given prime number "p", the "p"-adic order or additive "p"-adic valuation of a number "n" is the highest exponent ν such that "p"ν divides "n". It is commonly abbreviated ord"p"("n") or ν"p"("n"). The most important application of the "p"-adic order is in constructing the field of "p"-adic numbers. It is also applied toward various more elementary topics, such as the distinction between singly and doubly even numbers.

ee also

*Valuation (mathematics)
*Multiplicity
*Ostrowski's theorem
*"p"-adic numbers

References


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