## Missouri Journal of Mathematical Sciences

### 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

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

Digital Object Identifier
doi:10.35834/mjms/1312232719

Mathematical Reviews number (MathSciNet)
MR2650060

Zentralblatt MATH identifier
1247.11019

#### 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

#### References

• E. Barbeau, Pell's Equation, Springer, New York, 2003.
• A. T. Benjamin, S. S. Plott, and J. A. Sellers, Tiling Proofs of Recent Sum Identities Involving Pell Numbers, The Annals of Combinatorics, 12.3 (2008), 271–278.
• G. H. Hardy and E. M. Wright, An Introduction to The Theory of Numbers, Oxford University Press, Oxford, 1979.
• A. F. Horadam, Pell Identities, The Fibonacci Quarterly, 9.3 (1971), 245–252.
• N. Robbins, Beginning Number Theory, Wm. C. Brown Publishers, Dubuque, 1993.
• S. F. Santana and J. L. Díaz-Barrero, Some Properties of Sums Involving Pell Numbers, Missouri Journal of Mathematical Sciences, 18.1 (2006), 33–40.
• J. A. Sellers, Domino Tilings and Products of Fibonacci and Pell Numbers, Journal of Integer Sequences, 5.1 (2002).
• N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, published electronically at http://www.research.att.com/$\sim$njas/sequences/, 2006.