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Sums of Powers in Arithmetic Progressions

Published online by Cambridge University Press:  20 November 2018

Charles Small
Charles Small*
Affiliation:
Dept. of Mathematics, Queens University, Kingston, Ontario, Canada K7L 3N6
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The papers [2] and [3] study the function g(k, n), defined for integers k > 1 and n > 1 as the smallest r with the property that every integer is a sum of r kth powers mod n. This note identifies g′(k), defined as the maximum over all n of g(k, n), with the function Γ(k) studied by Hardy and Littlewood [1] fifty years ago in connection with Waring's problem.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 4 , 01 December 1978 , pp. 505 - 506
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Hardy, G. H., Littlewood, J. E., and Pôlya, G., Inequalities. Cambridge University Press, New York, 1934.Google Scholar
2. Menon, K. V., An inequality for elementary symmetric functions. Canad. Math. Bull. vol. 15 (1), 1972, 133-135.Google Scholar
3. Whiteley, J. N., A generalization of a Theorem of Newton. Proc. American Math. Soc. 13 (1962), 144-151.Google Scholar