منابع مشابه
Primes 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 کاملPrimes 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 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...
متن کاملPrime powers in elliptic divisibility sequences
Certain elliptic divisibility sequences are shown to contain only finitely many prime power terms. In some cases the methods prove that only finitely many terms are divisible by a bounded number of distinct primes.
متن کاملPrimitive divisors of elliptic divisibility sequences
Silverman proved the analogue of Zsigmondy’s Theorem for elliptic divisibility sequences. For elliptic curves in global minimal form, it seems likely this result is true in a uniform manner. We present such a result for certain infinite families of curves and points. Our methods allow the first explicit examples of the elliptic Zsigmondy Theorem to be exhibited. As an application, we show that ...
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ژورنال
عنوان ژورنال: LMS Journal of Computation and Mathematics
سال: 2001
ISSN: 1461-1570
DOI: 10.1112/s1461157000000772