NARAYANA'S COWS NUMBERS AS DIFFERENCES OF TWO PELL NUMBERS

Abdullah Çağman

NARAYANA'S COWS NUMBERS AS DIFFERENCES OF TWO PELL NUMBERS

Abstract

In this paper, we consider the Diophantine equation $P_n - P_m = N_k$ in positive integers $n, m$ and $k$ with $n > m \ge 1$, where $P_n$ is the $n$-th Pell number and $N_k$ is the $k$-th Narayana's cows number. We completely solve this equation by using a lower bound for linear forms in logarithms due to Matveev and a version of the Baker-Davenport reduction method due to Dujella and Peth\H{o}.

Keywords

References

BAKER, A. AND DAVENPORT, H., The equations 3x^2-2=y^2 and 8x^2-7=z^2, Q. J. Math. Oxford Ser. (2) 20 (1969), 129--137.
BRAVO, J. J. AND LUCA, F., On a conjecture about repdigits in k-generalized Fibonacci sequences, Publ. Math. Debrecen 82 (2013), no. 3-4, 623--639.
ÇAĞMAN, A., Repdigits as sums of three Half-companion Pell numbers, Miskolc Mathematical Notes, 24 (2023a), no. 2, 687-697.
ÇAĞMAN, A., On Repdigits as Product of Pell and Narayana Numbers, Turkish Journal of Science, 8 (2023b), no. 3, 102–106. DOI: 10.66833/TJOS-2023-0011.
ÇAĞMAN, A., An approach to Pillai's problem with the Pell sequence and the powers of 3, Miskolc Math. Notes 22 (2021), no. 2, 599--610.
DDAMULIRA, M., LUCA, F., AND RAKOTOMALALA, M., On a problem of Pillai with Fibonacci numbers and powers of 2, Proc. Indian Acad. Sci. Math. Sci. 127 (2017), no. 3, 411--421.
DDAMULIRA, M., On the problem of Pillai with Padovan numbers and powers of 3, Studia Sci. Math. Hungar. 56 (2019), no. 3, 364--379.
DUJELLA, A. AND PETHŐ, A., A generalization of a theorem of Baker and Davenport, Q. J. Math. 49 (1998), no. 195, 291--306.

Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Abdullah Çağman ^*
0000-0002-0376-7042
Türkiye

Publication Date

October 18, 2026

Submission Date

September 21, 2026

Acceptance Date

October 18, 2026

Published in Issue

Year 2026 Volume: 12 Number: 1

IZ

https://izlik.org/JA28KC54MK

Cite

RIS / Bibtex

APA

Çağman, A. (2026). NARAYANA’S COWS NUMBERS AS DIFFERENCES OF TWO PELL NUMBERS. Eastern Anatolian Journal of Science, 12(1), 32-36. https://izlik.org/JA28KC54MK

AMA

1.Çağman A. NARAYANA’S COWS NUMBERS AS DIFFERENCES OF TWO PELL NUMBERS. Eastern Anatolian Journal of Science. 2026;12(1):32-36. https://izlik.org/JA28KC54MK

Chicago

Çağman, Abdullah. 2026. “NARAYANA’S COWS NUMBERS AS DIFFERENCES OF TWO PELL NUMBERS”. Eastern Anatolian Journal of Science 12 (1): 32-36. https://izlik.org/JA28KC54MK.

EndNote

Çağman A (October 1, 2026) NARAYANA’S COWS NUMBERS AS DIFFERENCES OF TWO PELL NUMBERS. Eastern Anatolian Journal of Science 12 1 32–36.

IEEE

[1]A. Çağman, “NARAYANA’S COWS NUMBERS AS DIFFERENCES OF TWO PELL NUMBERS”, Eastern Anatolian Journal of Science, vol. 12, no. 1, pp. 32–36, Oct. 2026, [Online]. Available: https://izlik.org/JA28KC54MK

ISNAD

Çağman, Abdullah. “NARAYANA’S COWS NUMBERS AS DIFFERENCES OF TWO PELL NUMBERS”. Eastern Anatolian Journal of Science 12/1 (October 1, 2026): 32-36. https://izlik.org/JA28KC54MK.

JAMA

1.Çağman A. NARAYANA’S COWS NUMBERS AS DIFFERENCES OF TWO PELL NUMBERS. Eastern Anatolian Journal of Science. 2026;12:32–36.

MLA

Çağman, Abdullah. “NARAYANA’S COWS NUMBERS AS DIFFERENCES OF TWO PELL NUMBERS”. Eastern Anatolian Journal of Science, vol. 12, no. 1, Oct. 2026, pp. 32-36, https://izlik.org/JA28KC54MK.

Vancouver

1.Abdullah Çağman. NARAYANA’S COWS NUMBERS AS DIFFERENCES OF TWO PELL NUMBERS. Eastern Anatolian Journal of Science [Internet]. 2026 Oct. 1;12(1):32-6. Available from: https://izlik.org/JA28KC54MK