We discuss an elementary problem, initially proposed for the Romanian Mathematical Olympiad, which leads to interesting remarks of various nature. We relate the problem to the theory of linear recurrence sequences with non-constant coefficients and their p-adic behaviour. Our considerations can be applied to a larger set of similarlydefined recurrences.
On the integral values of a curious recurrence
Veneziano F.;Zannier U.
2022-01-01
Abstract
We discuss an elementary problem, initially proposed for the Romanian Mathematical Olympiad, which leads to interesting remarks of various nature. We relate the problem to the theory of linear recurrence sequences with non-constant coefficients and their p-adic behaviour. Our considerations can be applied to a larger set of similarlydefined recurrences.
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