Frobenius numbers of numerical semigroups generated by three consecutive squares or cubes. (Q896247)
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scientific article; zbMATH DE number 6518149
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Frobenius numbers of numerical semigroups generated by three consecutive squares or cubes. |
scientific article; zbMATH DE number 6518149 |
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Frobenius numbers of numerical semigroups generated by three consecutive squares or cubes. (English)
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9 December 2015
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The authors apply \textit{Ø. J. Rødseth}'s algorithm [J. Reine Angew. Math. 301, 171-178 (1978; Zbl 0374.10011)] to get explicit polynomial formulas for the Frobenius number \(F(S)\) of a numerical semigroup \(S\) generated by three consecutive squares or cubes. For example, if \(S\) is generated by \(n^3\), \((n+1)^3\), \((n+2)^3\) with \(n=18m>0\), then \[ F(S)=1.259.712m^5+320.760m^4+44.712m^3+4644m^2+154m-1. \]
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Frobenius numbers
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numerical semigroups
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Rødseth algorithm
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