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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 73 Issue: 3

On the Jacobsthal numbers which are the product of two Modified Pell numbers

Ahmet Daşdemir(KASTAMONU UNIVERSITY)0000-0001-8352-2020
Mehmet Varol(KASTAMONU UNIVERSITY)0009-0008-8462-5185
Sayfa
—
Yayın Tarihi
2024-09-27
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

These give intersections of the Modified Pell and Jacobsthal numbers too for the case where $ m = 1 $ or $ n = 1 $.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:This paper presents an analytic study of determining all the possible solutions of the Diophantine equations such that $ {q_k} = {J_m} {J_n} $ and $ {J_k} = {q_m} {q_n} $.
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Temel Bulgular & Veri:This paper presents an analytic study of determining all the possible solutions of the Diophantine equations such that $ {q_k} = {J_m} {J_n} $ and $ {J_k} = {q_m} {q_n} $.
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Sonuç & Katkı:These give intersections of the Modified Pell and Jacobsthal numbers too for the case where $ m = 1 $ or $ n = 1 $.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Modifed Pell number · Jacobsthal number · linear form in logarithm

Abstract

This paper presents an analytic study of determining all the possible solutions of the Diophantine equations such that $ {q_k} = {J_m} {J_n} $ and $ {J_k} = {q_m} {q_n} $. These give intersections of the Modified Pell and Jacobsthal numbers too for the case where $ m = 1 $ or $ n = 1 $.

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Bu Makaleye Atıf Yap

Daşdemir, A., Varol, M. (2024). On the Jacobsthal numbers which are the product of two Modified Pell numbers. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 3. https://doi.org/10.31801/cfsuasmas.1315051

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Kaynakça (16)

  1. Vajda, S., Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications, Courier Corporation, New York, 2008.
  2. Koshy, T., Pell and Pell-Lucas Numbers with Applications, Springer, New York, 2014.
  3. Horadam, A. F., Applications of modified Pell numbers to representations, Ulam Quarterly, 3(1) (1994), 34–53.
  4. Horadam, A. F., Jacobsthal representation numbers, Fibonacci Quart., 34(1) (1996), 40–54.
  5. Daşdemir, A., On the Pell, Pell-Lucas and Modified Pell numbers by matrix method, Applied Mathematical Sciences, 5(64) (2011), 3173–3181.
  6. Daşdemir, A., On the Jacobsthal numbers by matrix method, SDU Journal of Science Journal of Science, 7(1) (2012), 69–76.
  7. Daşdemir, A., A study on the Jacobsthal and Jacobsthal-Lucas numbers by matrix method, DUFED Journal of Sciences, 3(1) (2014), 13–18.
  8. Arslan, S., Köken, F., The Jacobsthal and Jacobsthal-Lucas numbers via square roots of matrices, Int. Math. Forum., 11(11) (2016), 513–520. http://doi.org/10.12988/imf.2016.6442
  9. Catarino, P., Campos, H., A note on Gaussian Modified Pell numbers, Journal of Information and Optimization Sciences, 39(6) (2018), 1363–1371. http://doi.org/10.1080/02522667.2018.1471267
  10. Radicic, B., On k-circulant matrices involving the Pell numbers, Results in Mathematics, 74(4) (2019), 200. https://doi.org/10.1007/s00025-019-1121-9
  11. Daşdemir, A., Mersene, Jacobsthal, and Jacobsthal-Lucas numbers with negative subscripts, Acta Math. Univ. Comenian., 88(1) (2019), 142–156.
  12. Soykan, Y., Göcen, M., Properties of hyperbolic generalized Pell numbers, Notes on Number Theory and Discrete Mathematics, 26(4) (2020), 136–153. http://doi.org/10.7546/nntdm.2020.26.4.136-153
  13. Uygun, S¸., The relations between bi-periodic Jacobsthal and bi-periodic Jacobsthal Lucas sequence, Cumhuriyet Science Journal, 42(2) (2021), 346–357. http://doi.org/10.17776/csj.770080
  14. Matveev, E. M., An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II, II. Izv. Math., 64(6) (2000), 1217–1269. http://doi.org/10.1070/IM2000v064n06ABEH000314
  15. Baker, A., Davenport, H., The equations $3x^2 − 2 = y^2$ and $8x^2 − 7 = z^2$, Quart. J. Math. Oxford Ser., 20(1) (1969), 129–137.
  16. Dujella, A., Pethö, A., A generalization of a theorem of Baker and Davenport, Quart. J. Math. Oxford Ser., 49(195) (1998), 291–306. https://doi.org/10.1093/qjmath/49.195.291