The Frobenius problem, sums of powers of integers, and recurrences for the Bernoulli numbers |
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Authors: | Hans J.H. Tuenter |
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Affiliation: | Schulich School of Business, York University, Toronto, Canada M3J 1P3 |
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Abstract: | 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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Keywords: | Frobenius problem Sums of powers of integers Bernoulli numbers |
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