Linear Combinations of Factorial and $S$-unit in a Ternary recurrence sequence with a double root
Year: 2025
Type: preprint
Abstract: Here, we show that if $u_n=n2^n\pm 1$, then the largest prime factor of $u_n\pm m!$ for $n\ge 0,~m\ge 2$ tends to infinity with $\max\{m,n\}$. In particular, the largest $n$ participating in the equation $u_n\pm m!=2^a3^b5^c7^d$ with $n\ge 1,~m\ge 2$ is $n=8$ for which $(8\cdot 2^8+1)-4!=3^4\cdot 5^2$.
Source: arXiv (Cornell University)
Authors: Luca, Florian, Noubissie, Armand
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979266228
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