Some experimental results on the Frobenius problem

Matthias Beck; David Einstein; Shelemyahu Zacks

paper

Some experimental results on the Frobenius problem

arXiv:math/0204036

Abstract

We study the Frobenius problem: given relatively prime positive integers $a_{1}, ..., a_{d}$ , find the largest value of t (the Frobenius number) such that $\sum_{k = 1}^{d} m_{k} a_{k} = t$ has no solution in nonnegative integers $m_{1}, ..., m_{d}$ . Based on empirical data, we conjecture that except for some special cases the Frobenius number can be bounded from above by $a_{1} a_{2} a_{3}^{5/4} - a_{1} - a_{2} - a_{3}$ .

10 pages, 3 figures