## Functiones et Approximatio Commentarii Mathematici

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

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

#### 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