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The Frobenius problem, sums of powers of integers, and recurrences for the Bernoulli numbers

โœ Scribed by Hans J.H. Tuenter

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
139 KB
Volume
117
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

In the Frobenius problem with two variables, one is given two positive integers a and b that are relative prime, and is concerned with the set of positive numbers NR that have no representation by the linear form ax + by in nonnegative integers x and y. We give a complete characterization of the set NR, and use it to establish a relation between the power sums over its elements and the power sums over the natural numbers. This relation is used to derive new recurrences for the Bernoulli numbers.

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