1990
DOI: 10.7146/math.scand.a-12330
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On formulas for the Frobenius number of a numerical semigroup.

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Cited by 85 publications
(69 citation statements)
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“…We note that if p = 3, then G 2 = G 0 and κ + λ ≥ 3, so that parts (i) and (ii) of Theorem 2.1 imply that g = G 0 (and hence also g = G 2 , as in part (iii)). For p > 3, the DIOPHANTINE FROBENIUS PROBLEM RELATED TO RIEMANN SURFACES 503 integer q = (p − 3)p + 1, if prime, is the largest such that κ + λ < p. Hence, we obtain an easy corollary.…”
Section: The Main Results Define the Functionmentioning
confidence: 99%
“…We note that if p = 3, then G 2 = G 0 and κ + λ ≥ 3, so that parts (i) and (ii) of Theorem 2.1 imply that g = G 0 (and hence also g = G 2 , as in part (iii)). For p > 3, the DIOPHANTINE FROBENIUS PROBLEM RELATED TO RIEMANN SURFACES 503 integer q = (p − 3)p + 1, if prime, is the largest such that κ + λ < p. Hence, we obtain an easy corollary.…”
Section: The Main Results Define the Functionmentioning
confidence: 99%
“…No general formula has been found so far for the case p ≥ 3. Moreover, as Curtis shows in [1], there is no closed formula of a certain type for p = 3. If we focus our attention on this case, then we can think of F as a correspondence that maps three relatively prime integers n 1 , n 2 , n 3 to a nonnegative integer F(n 1 , n 2 , n 3 ).…”
Section: Introductionmentioning
confidence: 99%
“…In actual, unlike Sylvester's elegant formula, there are no polynomial solutions for more than two integers [1]. In general, it is NP-hard to find the Frobenius numbers for the number of given integers [4].…”
Section: Introductionmentioning
confidence: 99%