Research Article

New Results on Negative-Indexed Pell Numbers via Matrix Methods

Volume: 46 Number: 4 December 30, 2025
İbrahim Gökcan *, Ümmügülsün Çağlayan , Ali Hikmet Değer
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EN

New Results on Negative-Indexed Pell Numbers via Matrix Methods

Abstract

In this study, we investigate the Pell and Pell–Lucas numbers sequences and construct matrices whose elements are defined using negative indices of these sequences through Binet’s formula. Identities involving negative-indexed Pell and Pell–Lucas numbers are derived using the determinants and traces of these matrices. Furthermore, we examine various powers of the constructed matrices and discuss related elementary matrix operations.

Keywords

Pell numbers, Pell-Lucas numbers, matrix theory

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Publication Date

December 30, 2025

Submission Date

April 11, 2025

Acceptance Date

December 20, 2025

Published in Issue

Year 2025 Volume: 46 Number: 4

DOI

https://doi.org/10.17776/csj.1674240

IZ

https://izlik.org/JA25UM74HA

Cite

RIS / Bibtex
APA
Gökcan, İ., Çağlayan, Ü., & Değer, A. H. (2025). New Results on Negative-Indexed Pell Numbers via Matrix Methods. Cumhuriyet Science Journal, 46(4), 902-910. https://doi.org/10.17776/csj.1674240
AMA
1.Gökcan İ, Çağlayan Ü, Değer AH. New Results on Negative-Indexed Pell Numbers via Matrix Methods. CSJ. 2025;46(4):902-910. doi:10.17776/csj.1674240
Chicago
Gökcan, İbrahim, Ümmügülsün Çağlayan, and Ali Hikmet Değer. 2025. “New Results on Negative-Indexed Pell Numbers via Matrix Methods”. Cumhuriyet Science Journal 46 (4): 902-10. https://doi.org/10.17776/csj.1674240.
EndNote
Gökcan İ, Çağlayan Ü, Değer AH (December 1, 2025) New Results on Negative-Indexed Pell Numbers via Matrix Methods. Cumhuriyet Science Journal 46 4 902–910.
IEEE
[1]İ. Gökcan, Ü. Çağlayan, and A. H. Değer, “New Results on Negative-Indexed Pell Numbers via Matrix Methods”, CSJ, vol. 46, no. 4, pp. 902–910, Dec. 2025, doi: 10.17776/csj.1674240.
ISNAD
Gökcan, İbrahim - Çağlayan, Ümmügülsün - Değer, Ali Hikmet. “New Results on Negative-Indexed Pell Numbers via Matrix Methods”. Cumhuriyet Science Journal 46/4 (December 1, 2025): 902-910. https://doi.org/10.17776/csj.1674240.
JAMA
1.Gökcan İ, Çağlayan Ü, Değer AH. New Results on Negative-Indexed Pell Numbers via Matrix Methods. CSJ. 2025;46:902–910.
MLA
Gökcan, İbrahim, et al. “New Results on Negative-Indexed Pell Numbers via Matrix Methods”. Cumhuriyet Science Journal, vol. 46, no. 4, Dec. 2025, pp. 902-10, doi:10.17776/csj.1674240.
Vancouver
1.İbrahim Gökcan, Ümmügülsün Çağlayan, Ali Hikmet Değer. New Results on Negative-Indexed Pell Numbers via Matrix Methods. CSJ. 2025 Dec. 1;46(4):902-10. doi:10.17776/csj.1674240

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