On prime powers in linear recurrence sequences
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AbstractIn this paper we consider the Diophantine equation $$U_n=p^x$$ U n = p x where $$U_n$$ U n is a linear recurrence sequence, p is a prime number, and x is a positive integer. Under some technical hypotheses on $$U_n$$ U n , we show that, for any p outside of an effectively computable finite set of prime numbers, there exists at most one solution (n, x) to that Diophantine equation. We compute this exceptional set for the Tribonacci sequence and for the Lucas sequence plus one.
2012 ◽
Vol 15
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pp. 360-373
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1996 ◽
Vol 39
(1)
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pp. 35-46
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NONLINEAR FILTRATION OF BINARY LINEAR RECURRENCE SEQUENCE WITH RANDOM DELAY AND RANDOM INITIAL PHASE
2019 ◽
Vol 78
(6)
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pp. 475-487
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2012 ◽
Vol 43
(3)
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pp. 397-406
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1985 ◽
Vol 15
(2)
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pp. 599-608
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