## Missouri Journal of Mathematical Sciences

- Missouri J. Math. Sci.
- Volume 22, Issue 1 (2010), 37-43.

### Extensions and Refinements of Some Properties of Sums Involving Pell Numbers

#### Abstract

Falcón Santana and Díaz-Barrero [*Missouri Journal of
Mathematical Sciences*, **18.1**, pp. 33-40, 2006] proved that the sum
of the first $4n+1$ Pell numbers is a perfect square for all $n \ge 0$. They
also established two divisibility properties for sums of Pell numbers with odd
index. In this paper, the sum of the first $n$ Pell numbers is characterized in
terms of squares of Pell numbers for any $n \ge 0$. Additional divisibility
properties for sums of Pell numbers with odd index are also presented, and
divisibility properties for sums of Pell numbers with even index are derived.

#### Article information

**Source**

Missouri J. Math. Sci., Volume 22, Issue 1 (2010), 37-43.

**Dates**

First available in Project Euclid: 1 August 2011

**Permanent link to this document**

https://projecteuclid.org/euclid.mjms/1312232719

**Digital Object Identifier**

doi:10.35834/mjms/1312232719

**Mathematical Reviews number (MathSciNet)**

MR2650060

**Zentralblatt MATH identifier**

1247.11019

**Subjects**

Primary: 11B39: Fibonacci and Lucas numbers and polynomials and generalizations

#### Citation

Bradie, Brian. Extensions and Refinements of Some Properties of Sums Involving Pell Numbers. Missouri J. Math. Sci. 22 (2010), no. 1, 37--43. doi:10.35834/mjms/1312232719. https://projecteuclid.org/euclid.mjms/1312232719