Pseudoprimes for Higher-Order Linear Recurrence Sequences
نویسندگان
چکیده
منابع مشابه
Pseudoprimes for Higher-order Linear Recurrence Sequences
With the advent of high-speed computing, there is a rekindled interest in the problem of determining when a given whole number N > 1 is prime or composite. While complex algorithms have been developed to settle this for 200-digit numbers in a matter of minutes with a supercomputer, there is a need for simpler, more practical algorithms for dealing with numbers of a more modest size. Such practi...
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Higher-Order Linear Ramified Recurrence (HOLRR) is a PTIME sound and complete typed lambda caluclus. Its terms are those of a linear (affine) λ-calculus – every variable occurs at most once – extended with a limited recursive scheme on a word algebra. Completeness for PTIME holds by embedding Leivant’s ramified recurrence on words into HOLRR. Soundness is established at all types – and not only...
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This paper continues the work begun by D. Shanks and myself in [1] where certain cubic recurrences were used to give a very strong primality test. A complete characterization of the pseudoprimes for this test is given in terms of the periods of the corresponding sequences. Then these results are used to produce various types of pseudoprimes. A discussion of open problems is included.
متن کاملPositivity Problems for Low-Order Linear Recurrence Sequences
We consider two decision problems for linear recurrence sequences (LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem (are all but finitely many terms of a given LRS positive?). We show decidability of both problems for LRS of order 5 or less, with complexity in the Counting Hierarchy for Positivity, and in polynomi...
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Sequences of integers satisfying linear recurrence relations have been studied extensively since the time of Lucas [5], notable contributions being made by Carmichael [2], Lehmer [4], Ward [11], and more recently by many others. In this paper we obtain a unified theory of the structure of recurrence sequences by examining the ratios of recurrence sequences that satisfy the same recurrence relat...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1990
ISSN: 0025-5718
DOI: 10.2307/2008447