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Sums of Powers of Integers

by A.F. Beardon

Year of Award: 1997

Publication Information: The American Mathematical Monthly, vol. 103, 1996, pp. 201-213

Summary: This paper generalizes the well-known fact that "the sum of the first \(n\) positive cubes is the square of the sum of the first \(n\) positive numbers."  The generalization examines any polynomial relationship between "the sum of the first \(n\) positive \(j\) th powers" and "the sum of the first \(n\) positive \(k\)th powers" for any \(j\) and \(k\).

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About the Author: A.F. Beardon was at Cambridge University at the time of publication

Subject classification(s): Algebra and Number Theory | Number Theory | Discrete Mathematics | Combinatorics | Index
Publication Date: 
Tuesday, September 23, 2008