Sum of cubes is square of sum

Edward Barbeau and Samer Seraj
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 19, 2013, Number 1, Pages 1—13
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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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  6. Mason, J. Generalizing “Sums of cubes equals to squares of sums”, The Mathematical Gazette, Vol. 85, March 2001, 50–58.
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  9. Segal, S. L. A Note on Pyramidal Numbers, The American Mathematical Monthly, Vol. 69, 1962, 637–638.

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Cite this paper

APA

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

Chicago

Barbeau, Edward, and Samer Seraj. “Sum of Cubes is Square of Sum.” Notes on Number Theory and Discrete Mathematics 19, no. 1 (2013): 1-13.

MLA

Barbeau, Edward, and Samer Seraj. “Sum of Cubes is Square of Sum.” Notes on Number Theory and Discrete Mathematics 19.1 (2013): 1-13. Print.

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