JP Journal of Algebra, Number Theory and Applications
Volume 5, Issue 1, Pages 147 - 161
(April 2005)
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THE LINEAR DIOPHANTINE PROBLEM OF FROBENIUS
Joseph Bak (U. S. A.)
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Abstract: If S = {a1, a2, ?, an} is a set of relatively prime positive integers, it is well known that any sufficiently large integer can be expressed as a nonnegative integral combination of the elements of S. The Frobenius problem consists of determining how large is sufficiently large. That is, find the smallest possible integer L = (a1, a2, ?, an) with the property that any number greater than or equal to it can be expressed as a nonnegative integral combination of a1, a2, ?, an. We review two classical approaches to the problem, and offer a third one. We then apply this latter approach to obtain simplified proofs for several known results and to obtain some new results. |
Keywords and phrases: Frobenius number. |
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