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Start Over Creator Carlip, Walter

1. Bounds for frequencies of residues of second-order recurrences modulo pr

Creator:
Carlip, Walter and Somer, Lawrence
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Lucas, Fibonacci, stability, uniform distribution, and recurrence
Language:
English
Description:
The authors examine the frequency distribution of second-order recurrence sequences that are not p-regular, for an odd prime p, and apply their results to compute bounds for the frequencies of p-singular elements of p-regular second-order recurrences modulo powers of the prime p. The authors’ results have application to the p-stability of second-order recurrence sequences.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Square-free Lucas $d$-pseudoprimes and Carmichael-Lucas numbers

Creator:
Carlip, Walter and Somer, Lawrence
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Lucas, Fibonacci, pseudoprime, and Fermat
Language:
English
Description:
Let $d$ be a fixed positive integer. A Lucas $d$-pseudoprime is a Lucas pseudoprime $N$ for which there exists a Lucas sequence $U(P,Q)$ such that the rank of $N$ in $U(P,Q)$ is exactly $(N - \varepsilon (N))/d$, where $\varepsilon $ is the signature of $U(P,Q)$. We prove here that all but a finite number of Lucas $d$-pseudoprimes are square free. We also prove that all but a finite number of Lucas $d$-pseudoprimes are Carmichael-Lucas numbers.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Symmetry of iteration graphs

Creator:
Carlip, Walter and Mincheva, Martina
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
digraph, iteration digrap, quadratic map, cycle, and tree
Language:
English
Description:
We examine iteration graphs of the squaring function on the rings $\mathbb{Z}/n\mathbb{Z}$ when $n = 2^{k}p$, for $p$ a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the graphs are not symmetric when $k=3$ and when $k\ge 5$ and are symmetric when $k = 4$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public