A note on a special case of the Frobenius problem

Amitabha Tripathi ()
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Amitabha Tripathi: Indian Institute of Technology

Indian Journal of Pure and Applied Mathematics, 2013, vol. 44, issue 3, 375-381

Abstract: Abstract For a set of positive and relative prime integers A = {a 1…,a k }, let Γ(A) denote the set of integers of the form a 1 x 1+…+a k x k with each x j ≥ 0. Let g(A) (respectively, n(A) and s(A)) denote the largest integer (respectively, the number of integers and sum of integers) not in Γ(A). Let S*(A) denote the set of all positive integers n not in Γ(A) such that n + Γ(A) \ {0} ⊂ Γ((A)\{0}. We determine g(A), n(A), s(A), and S*(A) when A = {a, b, c} with a | (b + c).

Keywords: Representable; Frobenius number (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s13226-013-0019-6

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