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A Diophantine problem of Frobenius in terms of the least common multiple

✍ Scribed by Marek Raczunas; Piotr Chrza̧stowski-Wachtel

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
414 KB
Volume
150
Category
Article
ISSN
0012-365X

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✦ Synopsis

The Diophantine Problem of Frobenius is to find a formula for the least integer not representable as a nonnegative linear form of positive integers. A reduction formula for the Diophantine Problem of Frobenius is presented. The formula can be applied whenever there are common divisors of the coefficients except for the whole set of them. The reduction formula is expressed in terms of the least common multiple of the coefficients. For some classes of coefficients this formula gives an exact answer for the problem of Frobenius, and these classes are fully characterized in the paper.

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