P-adic valuation

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In number theory, the p-adic valuation or p-adic order of an integer n is the exponent of the highest power of the prime number p that divides n. It is denoted ν p ( n ) {\displaystyle \nu _{p}(n)} . Equivalently, ν p ( n ) {\displaystyle \nu _{p}(n)} is the exponent to which p {\displaystyle p} appears in the prime factorization of n {\displaystyle n} . The p-adic valuation is a valuation and gives rise to an analogue of the usual absolute value, though unlike the latter, the p-adic absolute value is not Archimedean. Whereas the completion of the rational numbers with respect to the usual absolute value results in the real numbers...

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