Edward Barbeau and Samer Seraj

Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132

Volume 19, 2013, Number 1, Pages 1–13

**Full paper (PDF, 163 Kb)**

## Details

### Authors and affiliations

Edward Barbeau

*University of Toronto, Canada
*

Samer Seraj

*University of Toronto, Canada
*

### Abstract

Inspired by the fact that the sum of the cubes of the first *n* naturals is equal to the square of their sum, we explore, for each *n*, the Diophantine equation representing all non-trivial sets of *n* integers with this property. We find definite answers to the standard question of infinitude of the solutions as well as several other surprising results.

### Keywords

- Diophantine equation
- CS-set

### AMS Classification

- 11D25

### References

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*x*^{3}+*y*^{3}+*z*^{3}=*x*+*y*+*z*, Proceedings of the American Mathematical Society, Vol. 16, February 1965, 148–153. - Frolov, M. Égalités à deux degrés, Bulletin de la Société Mathématique de France, Vol. 17, 1889, 69–83.
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*x*^{3}+*y*^{3}+*z*^{3}=*x*+*y*+*z*, Proceedings of the American Mathematical Society, Vol. 17, 1966, 493–496. - Segal, S. L. A Note on Pyramidal Numbers, The American Mathematical Monthly, Vol. 69, 1962, 637–638.

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## Cite this paper

Barbeau, E., & Seraj, S. (2013). Sum of cubes is square of sum. *Notes on Number Theory and Discrete Mathematics*, 19(1), 1-13.