Which Second-order Linear Integral Recurrences Have Almost All Primes as Divisors?
نویسنده
چکیده
This paper will prove that essentially only the obvious recurrences have almost all primes as divisors. An integer n is a divisor of a recurrence if n divides some term of the recurrence. In this paper, "almost all primes" will be taken interchangeably to mean either all but finitely many primes or all but for a set of Dirichlet density zero in the set of primes. In the context of this paper, the two concepts become synonymous due to the Frobenius density theorem. Our paper relies on a result of A. Schinzel [2], whose paper uses "almost all" in the same sense. Let {wn} be a recurrence defined by the recursion relation
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تاریخ انتشار 2010