## Norm form equations with solutions taking values in a multi-recurrence

### Volume 198 / 2021

Acta Arithmetica 198 (2021), 427-438
MSC: 11D57, 11B37, 11J87.
DOI: 10.4064/aa200622-22-10
Published online: 8 February 2021

#### Abstract

We are interested in solutions of a norm form equation that takes values in a given multi-recurrence. We show that among the solutions there are only finitely many different values in each component which lie in the given multi-recurrence unless the recurrence is of a precisely described exceptional shape. This gives a variant of the question on arithmetic progressions in the solution set of norm form equations.