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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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

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

First available in Project Euclid: 28 March 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

perfect numbers sum of cubes


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.

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  • 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.