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arXiv · 1611.05618

Linear combinations of factorials in binary recurrence sequences

Sudhansu Sekhar Rout
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Abstract

Let $\{u_{n}\}_{n \geq 0}$ be a non-degenerate binary recurrence sequence with positive discriminant. In this paper, we consider the Diophantine equation $u_m + u_n = a_1 n_1! + \cdots + a_k n_k!$ 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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Sudhansu Sekhar Rout. 2016-11-17. Linear combinations of factorials in binary recurrence sequences. https://arxiv.org/abs/1611.05618

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