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Dergiler / Eastern Anatolian Journal of Science / 2026 / Volume: 12 Issue: 1

NARAYANA'S COWS NUMBERS AS DIFFERENCES OF TWO PELL NUMBERS

Abdullah Çağman(ERZURUM TECHNICAL UNIVERSITY)0000-0002-0376-7042
Sayfa
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Yayın Tarihi
2026-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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}.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı: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}.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Pell numbers · Narayana's cows sequence · Diophantine equation

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}.

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Bu Makaleye Atıf Yap

Çağman, A. (2026). NARAYANA'S COWS NUMBERS AS DIFFERENCES OF TWO PELL NUMBERS. Eastern Anatolian Journal of Science, Volume: 12 Issue: 1. https://ajindex.com/articles/1475618

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Kaynakça (10)

  1. 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.
  2. 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.
  3. ÇAĞMAN, A., Repdigits as sums of three Half-companion Pell numbers, Miskolc Mathematical Notes, 24 (2023a), no. 2, 687-697.
  4. 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.
  5. 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.
  6. 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.
  7. DDAMULIRA, M., On the problem of Pillai with Padovan numbers and powers of 3, Studia Sci. Math. Hungar. 56 (2019), no. 3, 364--379.
  8. DUJELLA, A. AND PETHŐ, A., A generalization of a theorem of Baker and Davenport, Q. J. Math. 49 (1998), no. 195, 291--306.
  9. HERNANDEZ HERNANDEZ, S., LUCA, F., AND RIVERA, L. M., On Pillai's problem with the Fibonacci and Pell sequences, Bol. Soc. Mat. Mex. 25 (2019), no. 3, 495--507.
  10. MATVEEV, E. M., An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers II, Izv. Math. 64 (2000), no. 6, 1217--1269. STROEKER, R. J. AND TIJDEMAN, R., Diophantine equations, In: Computational Methods in Number Theory, Part II, MC Tracts 155, Centre Math. Comp. Sci., Amsterdam, (1982), pp. 321--369.