Functiones et Approximatio Commentarii Mathematici

On the representation of an even perfect number as the sum of five cubes

Bakir Farhi

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Abstract

The aim of this note is to show that any even perfect number, other than $6$, can be written as the sum of at most five positive integral cubes. We also conjecture that any such number can even be written as the sum of at most three positive integral cubes.

Article information

Source
Funct. Approx. Comment. Math., Volume 57, Number 2 (2017), 277-278.

Dates
First available in Project Euclid: 28 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.facm/1490688028

Digital Object Identifier
doi:10.7169/facm/1639

Mathematical Reviews number (MathSciNet)
MR3732899

Zentralblatt MATH identifier
06864175

Subjects
Primary: 11A25: Arithmetic functions; related numbers; inversion formulas
Secondary: 11B13: Additive bases, including sumsets [See also 05B10]

Keywords
perfect numbers sum of cubes

Citation

Farhi, Bakir. On the representation of an even perfect number as the sum of five cubes. Funct. Approx. Comment. Math. 57 (2017), no. 2, 277--278. doi:10.7169/facm/1639. https://projecteuclid.org/euclid.facm/1490688028


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References

  • M.B. Nathanson, Additive Number Theory: The Classical Bases, Graduate Texts in Mathematics, Vol. 164, Springer-Verlag, New York, 1996.
  • W. Sierpiński, Elementary theory of numbers, Chap IV, Panstowowe Wydawnictwo Naukowe, Warsaw, 1964.