# zbMATH — the first resource for mathematics

Linear diophantine problems. (English) Zbl 0854.11016
Let $$A_k= \{a_1, \dots, a_k\}$$ be a set of natural numbers with $$\text{gcd} (a_1, \dots, a_k)=1$$. The greatest integer $$g= g(A_k)$$ with no representation $$g= \sum^k_{i=1} x_i a_i$$, $$x_i\in \mathbb{N}_0= \{0, 1, \dots\}$$ is called the Frobenius number of $$A_k$$. For a special class of sets $$A_k$$ we transform the problem of determining $$g(A_k)$$ to an equivalent one and get an algorithm whose number of arithmetical operations for computing $$g(A_k)$$ depends on $$k$$ only. Furthermore some new formulas for $$g(A_k)$$ in special cases are given.

##### MSC:
 11D04 Linear Diophantine equations
##### Keywords:
linear diophantine problems; Frobenius number
Full Text:
##### References:
 [1] P. T. Bateman, Remark on a recent note on linear forms. Amer. Math. Monthly65, 517-518 (1958). · Zbl 0083.03801 · doi:10.2307/2308578 [2] G. Hofmeister, Remark on linear forms. Arch. Math.65, 511-515 (1995). · Zbl 0858.11014 · doi:10.1007/BF01194169 [3] J. B. Roberts, Note on linear forms. Proc. Amer. Math. Soc.7, 465-469 (1956). · Zbl 0071.03902 · doi:10.1090/S0002-9939-1956-0091961-5
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.