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Difference between revisions of "Divisor (of an integer or of a polynomial)"

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''of an integer <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336901.png" />''
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"'''Divisor'''" may refer to:
  
An integer <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336902.png" /> which divides the number <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336903.png" /> without remainder. In other words, a divisor of the integer <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336904.png" /> is an integer <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336905.png" /> such that, for a certain integer <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336906.png" />, the equality <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336907.png" /> holds. A divisor of a polynomial <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336908.png" /> is a polynomial <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336909.png" /> that divides <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d03369010.png" /> without remainder (cf. [[Division|Division]]). More generally, in an arbitrary ring <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d03369011.png" /> a divisor of an element <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d03369012.png" /> is an element <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d03369013.png" /> such that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d03369014.png" /> for a certain <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d03369015.png" />.
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* a divisor of an integer or polynomial; see [[divisor (of an integer)]];
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* a divisor in a more general ring, or in algebraic geometry; see [[divisor(2)]].

Revision as of 01:07, 24 April 2012

"Divisor" may refer to:

How to Cite This Entry:
Divisor (of an integer or of a polynomial). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Divisor_(of_an_integer_or_of_a_polynomial)&oldid=16756
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article