Term and notation for the maximal exponent that gives a power of a number that divides some other number

Asked Mar 11 '24 at 01:25

Active Mar 11 '24 at 02:37

Viewed 13 times

Consider two integer numbers $a$ and $b$, and let $n$ be the maximal natural number (or $0$) such that $a^n$ still divides $b$. Is there some standard term and/or notation for this $n$ (as a function of $a$ and $b$)?

Of course, this notion applies not only to integers: $a$ and $b$ could be elements of any commutative ring or semi-ring, or of a commutative (multiplicative) monoid.

edited Mar 11 '24 at 02:37

Bill Dubuque

272,048

asked Mar 11 '24 at 01:25

Alexey

2,124

We write $a^n| b$ to indicate that $a^n$ exactly divides $b$; cf. this; also we write $n=v_a(b)$ – J. W. Tanner Mar 11 '24 at 01:30
Cf. p-adic valuation – J. W. Tanner Mar 11 '24 at 01:37

Term and notation for the maximal exponent that gives a power of a number that divides some other number

0 Answers0