Appearance of Primes in Fourth-Order Odd Divisibility Sequences
E. L. Roettger
Department of General Education
Mount Royal University
4825 Mount Royal Gate SW
Calgary, AB T3E 6K6
Canada
H. C. Williams
Department of Mathematics and Statistics
University of Calgary
2500 University Drive NW
Calgary, AB T2N 1N4
Canada
Abstract:
Let (An) denote any odd, non-degenerate,
non-null, fourth-order linear divisibility sequence and let p be
any prime such that p divides some term An
(n > 1) of (An). In this paper we
derive a number of properties of (An). In
particular, we exhibit conditions which guarantee that if p
| Ak, then ω | k. Here ω (=
ω(p)) is the least positive integer m such that p
| Am.
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(Concerned with sequences
A005013
A056570
A127595
A215465
A215466
A238536
A238537
A238538.)
Received April 7 2021; revised versions received June 5 2021; June 22 2021.
Published in Journal of Integer Sequences,
July 1 2021.
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