Namespaces
Variants
Actions

Difference between revisions of "Frobenius number"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
(TeX)
 
Line 1: Line 1:
Let <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f120/f120220/f1202201.png" /> be a finite set of positive integers with greatest common divisor <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f120/f120220/f1202202.png" />. The Frobenius number of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f120/f120220/f1202203.png" /> is the largest natural number that cannot be written as a linear integer combination of the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f120/f120220/f1202204.png" /> with non-negative coefficients.
+
{{TEX|done}}
 +
Let $S=\{a_1,\ldots,a_k\}$ be a finite set of positive integers with greatest common divisor $1$. The Frobenius number of $S$ is the largest natural number that cannot be written as a linear integer combination of the $a_i$ with non-negative coefficients.
  
 
See [[Frobenius problem|Frobenius problem]].
 
See [[Frobenius problem|Frobenius problem]].

Latest revision as of 15:24, 10 August 2014

Let $S=\{a_1,\ldots,a_k\}$ be a finite set of positive integers with greatest common divisor $1$. The Frobenius number of $S$ is the largest natural number that cannot be written as a linear integer combination of the $a_i$ with non-negative coefficients.

See Frobenius problem.

How to Cite This Entry:
Frobenius number. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Frobenius_number&oldid=15010
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article