Linear combinations of factorials in binary recurrence sequences

2016/11/17 by Sudhansu Sekhar Rout, Rout, Sudhansu Sekhar
Computer Science · Mathematics · Physics and Astronomy · #05A10 #11J86 #Advanced Mathematical Theories and Applications #Chaos-based Image/Signal Encryption #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Primary 11B39 #Secondary 11D61

paper · pdf · doi:10.48550/arxiv.1611.05618

openalex publication_date 2016/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \u_n\_{n ≥ 0} be a non-degenerate binary recurrence sequence with positive discriminant. In this paper, we consider the Diophantine equation u_m + u_n = a₁ n₁! + ⋯ + a_k n_k! and prove that there are only finitely many effectively computable terms which can be expressed as a sum of factorials. Furthermore, we find the terms of the balancing sequences that can be written as a sum of two factorials.

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