On a problem of Pillai involving S-units and Lucas numbers

2024/01/12 by Herbert Batte, Mahadi Ddamulira, Batte, Herbert +5
Physics and Astronomy · #11B39 #11D45 #11D61 #11Y50 #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2401.06555

openalex publication_date 2024/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \L_n\_{n≥ 0} be the sequence of Lucas numbers. In this paper, we look at the exponential Diophantine equation L_n-2^x3^y=c, for n,x,y∈ ℤ_≥0. We treat the cases c∈ -ℕ, c=0 and c∈ ℕ independently. In the cases that c∈ ℕ and c∈ -ℕ, we find all integers c such that the Diophantine equation has at least three solutions. These cases are treated independently since we employ quite different techniques in proving the two cases.

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