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We give explicit formulas for the p-Frobenius number of three consecutive squares, which is the largest integer that can only be represented in at most p ways by non-negative integer linear combinations of three consecutive square numbers. We also establish explicit formulas for the related values, including the p-genus, which is the number of integers that can only be represented in at most p ways by non-negative integer linear combinations of three consecutive square numbers.

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p-Frobenius Numbers of Numerical Semigroups Generated by Three Consecutive Squares

  • 会议论文

  • 发表日期：

    2025年

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  • Takao Komatsu,
  • Prapanpong Pongsriiam

摘要

We give explicit formulas for the p-Frobenius number of three consecutive squares, which is the largest integer that can only be represented in at most p ways by non-negative integer linear combinations of three consecutive square numbers. We also establish explicit formulas for the related values, including the p-genus, which is the number of integers that can only be represented in at most p ways by non-negative integer linear combinations of three consecutive square numbers.