**Publications **

#### 2017

#### Bakir FARHI

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

Functiones et Approximatio Commentarii Mathematici
vol: 57, pp: 277-278,
num: 2,
2017
.

**Keyword :**Perfect numbers, Sum of cubes

**URL :**https://projecteuclid.org/euclid.facm/1490688028

**Document**

#### 2014

#### Bakir FARHI

**An elementary proof that any natural number can be written as the sum of three terms of the sequence ⌊n^2/3⌋ **

Journal of integer sequences
vol: 17,
July 11,
2014
.

**Keyword :**Additive bases, sum of squares, The Gauss-Legendre theorem.

**Document**

#### 2013

#### Bakir FARHI

**Algebraic and topological structures on the set of mean functions and generalization of the AGM mean **

Colloquim Mathematicum
vol: 132, pp: 139-149,
2013
.

**Keyword :**Means, abelian groups, metric spaces, symmetries

**Document**

#### Bakir FARHI

**On the representation of the natural numbers as the sum of three terms of the sequence [n^2/a] **

Journal of Integer sequences
vol: 16,
2013
.

**Keyword :**Additive bases, Legendre's theorem

**Document**

#### 2012

#### Bakir FARHI

**A study of a curious arithmetic function **

Journal of Integer sequences
vol: 15,
2012
.

**Keyword :**Arithmetic function, least common multiple, 2-adic valuation

**Document**

#### 2011

#### Bakir FARHI

**An explicit formula generating the non-Fibonacci numbers **

Arxiv
arXiv: 1105.1127v2 (10 May 2011),
2011
.

**Keyword :**The complement of a sequence, non-Fibonacci numbers

**URL :**http://www.arxiv.org

**Document**

#### 2010

#### Bakir FARHI

** How to obtain the continued fraction convergents of the number e by neglecting integrals **

Arxiv
arXiv: 1005.2951v2 (19 May 2010),
2010
.

**Keyword :**Continued fractions, rational approximations, integrals with positive integrands

**URL :**http://www.arxiv.org

**Document**

#### Bakir FARHI

** An analog of the arithmetic triangle obtained by replacing the products by the least common multiples **

Arxiv
arXiv: 1002.1383v2 (9 Feb 2010),
2010
.

**Keyword :**Al-Karaji's triangle, least common multiple, binomial coefficients

**URL :**http://www.arxiv.org

**Document**

#### 2009

#### Bakir FARHI

** On the average asymptotic behavior of a certain type of sequences of integers **

Integers : Electronic Journal of Combinatorial Number Theory
vol: 9, pp: 555-567,
num: #A42,
2009
.

**Keyword :**Least common multiple, special sequences of integers, convergence in the average sense, irrational numbers

**URL :**http://www.integers-ejcnt.org/

**Document**