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Frobenius numbers of numerical semigroups generated by three consecutive squares or cubes

Abstract

We establish and prove polynomial formulas for the Frobenius numbers of numerical semigroups generated by \(n^2, (n+1)^2, (n+2)^2\) and by \(n^3, (n+1)^3, (n+2)^3\). The formulas depend on the residue class of \(n\) modulo 4 and 18, respectively.

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Correspondence to Irena Swanson.

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Communicated by Fernando Torres.

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Lepilov, M., O’Rourke, J. & Swanson, I. Frobenius numbers of numerical semigroups generated by three consecutive squares or cubes. Semigroup Forum 91, 238–259 (2015). https://doi.org/10.1007/s00233-014-9687-8

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Keywords

  • Frobenius number
  • Numerical semigroup
  • Rødseth’s algorithm