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Linear combinations of factorial and S-unit in a ternary recurrence sequence with a double root
Journal article   Peer reviewed

Linear combinations of factorial and S-unit in a ternary recurrence sequence with a double root

Florian Luca and Armand Noubissie
Periodica mathematica Hungarica, Vol.86(2), pp.422-441
01/06/2023
DOI: https://doi.org/10.1007/s10998-022-00481-7

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
Here, we showthat if un = n2(n) +/- 1, then the largest prime factor of u(n) +/- m! for n >= 0, m >= 2 tends to infinity with max{m, n}. In particular, the largest n participating in the equation u(n) +/- m! = 2(a)3(b)5(c)7(d) with n >= 1, m >= 2 is n = 8 for which (8.2(8) + 1) - 4! = 3(4).5(2).

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