Some estimated formulas for the Frobenius numbers. (English) Zbl 0856.11013
If \(a_0< a_1< \dots< a_s\) are integers with gcd \((a_0, a_1, \dots, a_s)=1\) and \(a_i \not\equiv a_j \pmod {a_0}\) for any \(i\neq j\), then a generalization of Vitek’s bound of the Frobenius number \(g(a_0, a_1, \dots, a_n)\) is given. If \(a_0\) is prime it is shown that
\[
g(a_0, a_1, \dots, a_n) \leq \biggl\lfloor {{a_0 -2} \over 2}+1 \biggr\rfloor (a_s- s)- 1.
\]
Some other bounds are given in the cases \(s=3\) and \(s=2\).
Reviewer: J.Piehler (Merseburg)
References:
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