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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

n-tuples of positive integers with the same sum and the same product


Authors: Yong Zhang and Tianxin Cai
Journal: Math. Comp. 82 (2013), 617-623
MSC (2010): Primary 11D25; Secondary 11D72, 11G05
Published electronically: May 8, 2012
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Abstract: In this paper, by using the theory of elliptic curves, we prove that for every $ k$, there exists infinitely many primitive sets of $ k$ $ n$-tuples of positive integers with the same sum and the same product.


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Additional Information

Yong Zhang
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China
Email: zhangyongzju@163.com

Tianxin Cai
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China
Email: txcai@zju.edu.cn

DOI: http://dx.doi.org/10.1090/S0025-5718-2012-02609-3
PII: S 0025-5718(2012)02609-3
Keywords: $n$-tuples, the system of equations, elliptic curves
Received by editor(s): April 20, 2011
Received by editor(s) in revised form: August 19, 2011
Published electronically: May 8, 2012
Additional Notes: This research was supported by China National Science Foundation Grant No.10871169.
Article copyright: © Copyright 2012 American Mathematical Society