The Diophantine equation a ((b^k-1)/(b-1)) = U_n-U_m

2023/06/06 by Pagdame Tiebekabe, Ismaïla Diouf, Tiebekabe, P. +5
Physics and Astronomy · #11B39 #11D61 #11J86 #11Y50 #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2306.04022

openalex publication_date 2023/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Here, we find all positive integer solutions of the Diophantine equation in the title, where (U_n)_{n\geqslant 0} is the generalized Lucas sequence U₀=0, U₁=1 and U_n+1=r U_n +s U_n-1 with r and s integers such that Δ= r² +4 s >0.

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