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Reverted edits by JoshC (talk) to last revision by Tzoran
Given a [[prime number]] p, the '''p-adic value''' is the function, denoted <math>v_p</math>, which takes as its argument a natural number n and returns the power of p appearing in the [[prime factorization]] of that number (equivalently, the highest power of p which divides n):
Given a [[prime number]] p, the '''p-adic value''' is the function, denoted <math>v_p</math>, which takes as its argument a natural number n and returns the power of p appearing in the [[prime factorization]] of that number (equivalently, the highest power of p which divides n):
<math>v_p(x)=\max\{n:p^n\mid x\}</math>. For example, the p-adic values of 60 for p=2,3,5,7,11,13... are 2,1,1,0,0,0,.... One can associate with the p-adic valuation an absolute value <math>|n|_p=p^{-v_P(n)}</math>.
<math>v_p(x)=\max\{n:p^n\mid x\}</math>. For example, the p-adic values of 60 for p=2,3,5,7,11,13... are 2,1,1,0,0,0,.... One can associate with the p-adic valuation an absolute value <math>|n|_p=p^{-v_P(n)}</math>.
[[Category:Mathematics]]
[[Category:Mathematics]]
[[Category:Algebra]]
[[Category:Algebra]]