Abstract
It is proved that every simple linear recurrence defined over a number field K, that has zeros modulo almost all prime ideals of K, takes the value 0 for a certain integer index. A similar theorem does not hold, in general, for simple linear recurrences of order n > 3. The case n = 3 is studied, but not decided.
To Professor Robert Tichy on his 60th anniversary
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Schinzel, A. (2017). On Simple Linear Recurrences. In: Elsholtz, C., Grabner, P. (eds) Number Theory – Diophantine Problems, Uniform Distribution and Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-55357-3_20
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DOI: https://doi.org/10.1007/978-3-319-55357-3_20
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