대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제57권3호
  • /
  • Pages.623-647
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  • 2020
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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THE FROBENIUS PROBLEM FOR NUMERICAL SEMIGROUPS GENERATED BY THE THABIT NUMBERS OF THE FIRST, SECOND KIND BASE b AND THE CUNNINGHAM NUMBERS

  • Song, Kyunghwan (Institute of Mathematical Sciences Ewha Womans University)
  • 투고 : 2019.04.15
  • 심사 : 2019.12.18
  • 발행 : 2020.05.31
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초록

The greatest integer that does not belong to a numerical semigroup S is called the Frobenius number of S. The Frobenius problem, which is also called the coin problem or the money changing problem, is a mathematical problem of finding the Frobenius number. In this paper, we introduce the Frobenius problem for two kinds of numerical semigroups generated by the Thabit numbers of the first kind, and the second kind base b, and by the Cunningham numbers. We provide detailed proofs for the Thabit numbers of the second kind base b and omit the proofs for the Thabit numbers of the first kind base b and Cunningham numbers.

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참고문헌

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