On the Exponential Diophantine Equation (F_m+1^(k))^x-(F_m-1^(k))^x = F_n^(k)

2022/05/26 by Hayat Bensella, Bensella, Hayat, Bijan Kumar Patel +3
Mathematics · #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2205.13168

Abstract

In this paper, we explicitly find all solutions of the title Diophantine equation, using lower bounds for linear forms in logarithms and properties of continued fractions. Further, we use a version of the Baker-Davenport reduction method in Diophantine approximation, due to Dujella and Pethö. This paper extends the previous work of \citePatel.

Related

• On the Diophantine equation F_n-F_m=2^a
• An exponential Diophantine equation related to the difference between\n powers of two consecutive Balancing numbers
• On the Diophantine Equation F_n = F_l^k (F_l^m-1)
• On solutions of the Diophantine equation P_m-L_n=c
• On the Non-negative Integer Solutions to Diophantine Equations F_n - F_m = 7^a and F_n - F_m = 13^a