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Frobenius number

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.

Noun

Frobenius number (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.

Forms of Frobenius number

pluralFrobenius numbers

Origin of Frobenius number

After Ferdinand Georg Frobenius.

Questions about Frobenius number

What does Frobenius number mean?
Frobenius number means 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.
What part of speech is Frobenius number?
Frobenius number is a noun.
What is the plural of Frobenius number?
The plural of Frobenius number is Frobenius numbers.

Words near Frobenius number in the dictionary

  1. Frobenius
  2. Frobenius covariant
  3. Frobenius covariants
  4. Frobenius endomorphism
  5. Frobenius endomorphisms
  6. Frobenius number
  7. Frobenius numbers
  8. Froberg
  9. Frobergs
  10. Frobisher
  11. Frobisher Bay

Source and license

Adapted from Wiktionary: Frobenius number (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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