# Positive Frobenius Numbers of Three Arguments

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Let , , be three positive integers with . It is well-known that all sufficiently large integers are representable as positive linear combinations of , , . Consider , the positive Frobenius number of , , , defined to be the largest integer not representable as a positive linear combination of , , . Then is the usual Frobenius number, that is, the largest integer not representable as a non-negative linear combination , , . ( differs from the positive Frobenius number in that multipliers for linear combinations of larger integers are allowed to be zero.) The function corresponds to the *Mathematica* built-in function FrobeniusNumber[a,b,c].

Contributed by: Abdelwaheb Miled (March 2011)

Open content licensed under CC BY-NC-SA

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S. M. Johnson, "A Linear Diophantine Problem," *Canadian Journal of Mathematics*, 12, 1960 pp. 390–398.

A. Miled, "On a Problem of Frobenius in Three Numbers," arXiv.org, 2009.

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