Prime divisors of second order linear recurrences. II
نویسندگان
چکیده
منابع مشابه
Second-order Linear Recurrences of Composite Numbers
In a well-known result, Ronald Graham found a Fibonacci-like sequence whose two initial terms are relatively prime and which consists only of composite integers. We generalize this result to nondegenerate second-order recurrences.
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For f(x) ∈ Z[x] and a ∈ Z, we let f(x) be the nth iterate of f(x), P (f, a) = {p prime : p|f(a) for some n}, and D(P (f, a)) denote the natural density of P (f, a) within the set of primes. A conjecture of Jones [5] indicates that D(P (f, a)) = 0 for most quadratic f . In this paper, we find an exceptional family of (f ,a) such that D(P (f, a)) > 0 by considering ft(x) = (x + t) − 2 − t and at ...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1976
ISSN: 0022-314X
DOI: 10.1016/0022-314x(76)90011-1