An Optimal Lower Bound for the Frobenius Problem

Iskander Aliev; Peter Gruber

An Optimal Lower Bound for the Frobenius Problem

Number Theory 2007-05-23 v4

Authors: Iskander Aliev , Peter Gruber

Abstract

Given $N$ positive integers $a_1, ..., a_N$ with $\gcd(a_1, ..., a_N)=1$ , let $f_N$ denote the largest natural number which is not a positive integer combination of $a_1, ..., a_N$ . This paper gives an optimal lower bound for $f_N$ in terms of the absolute inhomogeneous minimum of the standard $(N-1)$ -simplex.

Keywords

combinatorial bounds and extremal problems bound number theory

Cite

@article{arxiv.math/0512083,
  title  = {An Optimal Lower Bound for the Frobenius Problem},
  author = {Iskander Aliev and Peter Gruber},
  journal= {arXiv preprint arXiv:math/0512083},
  year   = {2007}
}

Comments

10 pages

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