Frobenius number

noun

For a given set of coprime positive integers, the greatest integer that cannot be expressed as a linear combination (with nonnegative integer coefficients) of its elements.

“The Frobenius number of 2 and 5 is 3, since 3 cannot be formed as a sum of twos and fives while every larger integer can.”

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Meanings

nounFrobenius number (plural Frobenius numbers)

plural Frobenius numbers

  1. For a given set of coprime positive integers, the greatest integer that cannot be expressed as a linear combination (with nonnegative integer coefficients) of its elements.

    The Frobenius number of 2 and 5 is 3, since 3 cannot be formed as a sum of twos and fives while every larger integer can.

Origin

After Ferdinand Georg Frobenius.

Full word history & related roots →
Cite this entry
APA

Frobenius number. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Frobenius%20number

MLA

“Frobenius number.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Frobenius%20number. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Frobenius number,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Frobenius%20number.

Source: Frobenius number on Wiktionary, CC BY-SA 4.0.