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# N-tuples of Positive Integers with the Same Sum and the Same Product

@article{Zhang2013NtuplesOP, title={N-tuples of Positive Integers with the Same Sum and the Same Product}, author={Yong Zhang and Tianxin Cai}, journal={Math. Comput.}, year={2013}, volume={82}, pages={617-623} }

- Published 2013 in Math. Comput.
DOI:10.1090/S0025-5718-2012-02609-3

It is proved that for every k there exist k triples of positive integers with the same sum and the same product. In this paper we solve the problem D.16 from the book [1] by proving the following Theorem. For every k there exist infinitely many primitive sets of k triples of positive integers with the same sum and the same product. (A set S of triples is called primitive if the greatest common divisor of all elements of all triples of S is 1.) Lemma. The system of equations (1) x1 + x2 + x3… CONTINUE READING