Missouri Journal of Mathematical Sciences

Extensions and Refinements of Some Properties of Sums Involving Pell Numbers

Brian Bradie

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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


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References

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