On a Variation of the Coin Exchange Problem for Arithmetic Progressions
نویسنده
چکیده
Let a1, a2, . . . , ak be relatively prime, positive integers arranged in increasing order. Let Γ denote the positive integers in the set { a1x1 + a2x2 + · · ·+ akxk : xj ≥ 0 }. Let S(a1, a2, . . . , ak) . = {n / ∈ Γ : n+ Γ ⊆ Γ }. We determine S(a1, a2, . . . , ak) in the case where the aj’s are in arithmetic progression. In particular, this determines g(a1, a2, . . . , ak) in this particular case.
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