Some experimental results on the Frobenius problem
Matthias Beck, David Einstein, Shelemyahu Zacks
Abstract
We study the Frobenius problem: given relatively prime positive integers a1,...,ad, find the largest value of t (the Frobenius number) such that Σk=1d mk ak = t has no solution in nonnegative integers m1,...,md. Based on empirical data, we conjecture that except for some special cases the Frobenius number can be bounded from above by a1 a2 a35/4 - a1 - a2 - a3.
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