KaydedilenlerDerginizi ekleyin

Dergiler / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 3

On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$

Alain TOGBE
Salah Eddine RIHANE
Bernadette FAYE
Florian LUCA
Sayfa
1640–1649
Yayın Tarihi
2022-11-04
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this paper, we find all the solutions of the title Diophantine equation in nonnegative integer variables(m, n, x) , where $P_k$ is the k th term of the Pell sequence.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we find all the solutions of the title Diophantine equation in nonnegative integer variables(m, n, x) , where $P_k$ is the k th term of the Pell sequence.
📊
Temel Bulgular & Veri:In this paper, we find all the solutions of the title Diophantine equation in nonnegative integer variables(m, n, x) , where $P_k$ is the k th term of the Pell sequence.
💡
Sonuç & Katkı:In this paper, we find all the solutions of the title Diophantine equation in nonnegative integer variables(m, n, x) , where $P_k$ is the k th term of the Pell sequence.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, we find all the solutions of the title Diophantine equation in nonnegative integer variables(m, n, x) , where $P_k$ is the k th term of the Pell sequence.

🔖

Bu Makaleye Atıf Yap

TOGBE, A., RIHANE, S. E., FAYE, B., LUCA, F. (2022). On the exponential Diophantine equation $P_n^x+P_{n+1}^x=P_m$. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 3, 1640–1649. https://ajindex.com/articles/607704

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (9)

  1. Baker A, Davenport H. The equations 3x2 􀀀 2 = y2 and 8x2 􀀀 7 = z2. Quarterly Journal of Mathematics 1969; 20: 129-137
  2. Bertók C, Hajdu L, Pink I, Rábai Z. Linear combinations of prime powers in binary recurrence sequences. International Journal of Number Theory 2017; 13: 261-271
  3. Bravo JJ, Luca F. Coincidences in generalized Fibonacci recurrences. Journal of Number Theory 2013; 133: 2121-2137
  4. Dujella A, Pethő A. A generalization of a theorem of Baker and Davenport. Quarterly Journal of Mathematics 1998; 49 (2): 291-306
  5. Luca F, Oyono R. An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers. Proceedings of the Japan Academy Series A 2011; 87: 45-50
  6. Marques D, Togbé A. On the sum of powers of two consecutive Fibonacci numbers. Proceedings of the Japan Academy Series A 2010; 86: 174-176
  7. Matveev EM. An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers, II. Izvestiya Mathematics 2000; 64: 1217-1269
  8. Ruiz CAG, Luca F. An exponential Diophantine equation related to the sum of powers of two consecutive k - generalized Fibonacci numbers. College Mathematics Journal 2014; 137: 171-188
  9. Shorey TN, Tijdeman R. Exponential Diophantine Equations. Cambridge, UK: Cambridge University Press, 1986.