Note on divisibility sequences
نویسندگان
چکیده
منابع مشابه
Primes in Divisibility Sequences
We give an overview of two important families of divisibility sequences: the Lehmer–Pierce family (which generalise the Mersenne sequence) and the elliptic divisibility sequences. Recent computational work is described, as well as some of the mathematics behind these sequences.
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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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Article history: Received 9 October 2015 Received in revised form 24 November 2015 Accepted 26 November 2015 Available online 8 January 2016 Communicated by Steven J. Miller MSC: 11B39
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Let R be an integral domain in which every two nonzero elements have a greatest common divisor. Let (an)n>1 be a sequence of nonzero elements in R. We prove that gcd(an, am) = agcd(n,m) for all n,m > 1 if and only if an = ∏
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1936
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1936-06435-9