On solutions of the Diophantine equation $L_n\pm L_m=p^a$:

S. C.  Patel; S. G.  Rayaguru; Pagdame Tiebekabe; G. K.  Panda; K. R.  KAKANOU

doi:10.26637/mjm1103/006

Abstract

Lucas sequence is one of the most studied binary recurrence sequence defined by the relation $L_{n+2}=L_{n+1}+L_n;~L_0=2, L_1=1$. In this paper, we investigate all the sums and differences of two Lucas numbers that are powers of a odd prime $p$ satisfying $p<10^3$.

Keywords:

Fibonacci numbers, Lucas numbers, linear forms in logarithms, Baker's method, reduction method

Mathematics Subject Classification:

11B39, 11D72, 11J86

Authors Imprint References Funding Related Articles Downloads

S. C. Patel Department of Mathematics National Institute of Technology Rourkela, Odisha, India.
S. G. Rayaguru Centre for Data Science Siksha 'O' Anusandhan University Bhubaneswar, Odisha, India.
Pagdame Tiebekabe Cheikh Anta Diop University, Faculty of Science, Department of Mathematics and Computer science, Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications (LACGAA) Dakar, Senegal.
G. K. Panda Department of Mathematics National Institute of Technology, Rourkela, Odisha, India.
K. R. KAKANOU Cheikh Anta Diop University, Faculty of Science, Department of Mathematics and Computer science, Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications (LACGAA) Dakar, Senegal.

Pages: 294-302
Date Published: 01-07-2023
Vol. 11 No. 03 (2023): Malaya Journal of Matematik (MJM)

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