Sum of terms of recurrence sequences and S-units in the solution sets of norm form equations

2024/10/02 by N, Darsana, Rout, S. S.
#11B37 #11D57 #11D61 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2410.01688

Abstract

In this paper, we prove two results related to the solutions of norm form equations. Firstly, we give a finiteness result for sums of terms of linear recurrence sequences appearing in the coordinates of solutions of norm form equations. Next, we give a finiteness result concerning solutions of norm form equations representable as sums of S-units with a fixed number of terms. To prove these results, we use a deep results concerning the finiteness of the solutions of polynomial-exponential equations and S-unit equations.

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