This article is cited in 1 paper

On the Frobenius problem for three arguments

I. S. Vorob'ev

Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences

Abstract: Asymptotic formulae for the mean values of various characteristics of the additive semigroup generated by three positive integers are obtained theoretically, the first of which is a formula for the number of integers not belonging to this semigroup. A numerical experiment is described which validates the results obtained.
Bibliography: 21 titles.

Keywords: continued fractions, Frobenius numbers, Kloostermann sums, double-circuit networks.

UDC: 511.335+517.524

MSC: Primary 11D07; Secondary 11Y99

Received: 31.03.2014 and 16.12.2015

DOI: 10.4213/sm8370

 English version: Sbornik: Mathematics, 2016, 207:6, 816–840

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