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}
}
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