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Abstract: For Lucas sequences of the first kind u n and second kind v n defined asusual for positive n by u n=a^n-b^n-a-b, v n=a^n+b^n, where a and b areeither integers or conjugate quadratic integers, we describe the set of indicesn for which n divides u n and also the set of indices n for which n dividesv n. Building on earlier work, particularly that of Somer, we show that thenumbers in these sets can be written as a product of a so-called basic number,which can only be 1, 6 or 12, and particular primes, which are describedexplicitly. Some properties of the set of all primes that arise in this way isalso given, for each kind of sequence.



Autor: Chris Smyth

Fuente: https://arxiv.org/







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