A new variant of the HilbertWaring problem
Authors:
Tianxin Cai and Deyi Chen
Journal:
Math. Comp. 82 (2013), 23332341
MSC (2010):
Primary 11P05; Secondary 11D85, 11D72
Published electronically:
March 5, 2013
MathSciNet review:
3073204
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Abstract: In this paper, we propose a new variant of Waring's problem: to express a positive integer as a sum of positive integers whose product is a th power. We define, in a similar way to that done for and in Waring's problem, numbers and . We obtain , for primes , for odd primes . Moreover, we obtain several interesting results and make two conjectures about and .
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Additional Information
Tianxin Cai
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou, 310027, China
Email:
txcai@zju.edu.cn
Deyi Chen
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou, 310027, China
Email:
chendeyi1986@126.com
DOI:
http://dx.doi.org/10.1090/S002557182013026853
Received by editor(s):
September 4, 2011
Received by editor(s) in revised form:
January 22, 2012, January 27, 2012, and February 1, 2012
Published electronically:
March 5, 2013
Additional Notes:
Project supported by China National Science Foundation Grant No.10871169.
Article copyright:
© Copyright 2013
American Mathematical Society
