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.
متن کاملStrong divisibility and lcm-sequences
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 = ∏
متن کاملPrimes in Elliptic Divisibility Sequences
Morgan Ward pursued the study of elliptic divisibility sequences initiated by Lucas, and Chudnovsky and Chudnovsky suggested looking at elliptic divisibility sequences for prime appearance. The problem of prime appearance in these sequences is examined here from a theoretical and a practical viewpoint. We exhibit calculations, together with a heuristic argument, to suggest that these sequences ...
متن کاملRigid Divisibility Sequences Generated by Polynomial Iteration
The goal of this thesis is to explore the properties of a certain class of sequences, rigid divisibility sequences, generated by the iteration of certain polynomials whose coefficients are algebraic integers. The main goal is to provide, as far as is possible, a classification and description of those polynomials which generate rigid divisibility sequences.
متن کاملPrime power terms in elliptic divisibility sequences
We study a problem on specializations of multiples of rational points on elliptic curves analogous to the Mersenne problem. We solve this problem when descent via isogeny is possible by giving explicit bounds on the indices of prime power terms in elliptic divisibility sequences associated to points in the image of a nontrivial isogeny. We also discuss the uniformity of these bounds assuming th...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2012
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa156-2-5