Divisibility Properties of Recurrent Sequences
نویسندگان
چکیده
منابع مشابه
On Divisibility Properties of Sequences of Integers
Let a 1 < a, < . . . be an infinite sequence of integers of positive lower logarithmic density, in other words 1 (1) lim sup > 0. X=+logxa;<x a i DAVENPORT and ERDŐS [1] proved that then there exists an infinite subsequence a,,, < a„, ` . . . satisfying a,, ./a,, .+, . In this note we will give various sharpenings of this result . The sequence a1 < a2 < . . . will be denoted by A, an infinite s...
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There are many different ways of defining a sequence in terms of solutions to difference equations. In fact, if a sequence satisfies one recurrence then it satisfies an infinite number of recurrences. Arithmetic properties of an integral sequence are often studied by direct methods based on the combinatorial or algebraic definition of the numbers or using their generating function. The rational...
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Note that, by (4 .4) and (4 .5), (7 .6) holds for all nonnegatíve p. Substituting from (7 .6) in (6 .1) and (6 .2) and evaluating coefficients of xm, we obtain the following two identities. r-1 m (p + q)T rP~+4) = pTrpm + ~,(q) + T (P)-L q r, m pq E a l i r-a-1, m-j s-0 j-0 r-1 m-1 pq ~-~ T(P)Tr(9a-l. m-i-1 a L-0 i-0 r-1 m (r + i)Tr m+q) _ (r + 1)Tr + p (r-s)T (P)T (q) a. j r-8-1, M-j 8-0 j-0 r...
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Throughout this paper c , e , . . . will denote positive constants, not neeessavily the swine at each occurrence . line inf [A (x)/x] mill be called N the lower density of the sequence .1., v1 m -ill denote numbers which can be chosen rbitrarily small not necessarily the swine at each occurrence, (',, . . . unnibers which can be chosen arbitrarily large . ri nat ui nd question now was : : Ahat ...
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ژورنال
عنوان ژورنال: Nonlinear Analysis: Modelling and Control
سال: 2008
ISSN: 2335-8963,1392-5113
DOI: 10.15388/na.2008.13.4.14554