Jump to content

Multiplicative partition

From Wikipedia, the free encyclopedia
This is an old revision of this page, as edited by Richard L. Peterson (talk | contribs) at 23:25, 17 December 2007 (work in progress, intend to add refs from american mathematical monthly and hopefully elsewhere.). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.
(diff) ← Previous revision | Latest revision (diff) | Newer revision → (diff)

Multiplicative partition (Number theory)

In number theory, a multiplicative partition of an integer n greater than 1 is a way of writing n as a product of integers greater than 1. The number n itself is considered as one of those products.

Examples=

  • 2*2*5, 2*10, 4*5, and 20 are the four multiplicative partitions of 20.
  • 3*3*3*3, 3*3*9, 3*27, 9*9, and 81 are the five multiplicative permutations of 81 = 3^4. Because 81 is the fourth power of a prime, 81 has the same number (5) of multiplicative partitions as the number four has of additive partitions.
  • 30 = 2*3*5 = 2*15 = 6*5 = 3*10 = 30 has five partitions.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Multiplicative_partition&oldid=178602765"