p-adic order

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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.

[edit] See also

• Valuation (mathematics)
• Multiplicity
• p-adic numbers