Affiliation:
1. Department of Mathematical Sciences, School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
Abstract
For given positive integers a1,a2,⋯,ak with gcd(a1,a2,⋯,ak)=1, the denumerant d(n)=d(n;a1,a2,⋯,ak) is the number of nonnegative solutions (x1,x2,⋯,xk) of the linear equation a1x1+a2x2+⋯+akxk=n for a positive integer n. For a given nonnegative integer p, let Sp=Sp(a1,a2,⋯,ak) be the set of all nonnegative integer n’s such that d(n)>p. In this paper, by introducing the p-numerical semigroup, where the set N0\Sp is finite, we give explicit formulas of the p-Frobenius number, which is the maximum of the set N0\Sp, and related values for the triple of arithmetic progressions. The main aim is to determine the elements of the p-Apéry set.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
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