J. Saunders

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20182025

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math.NT2025

Residues of Terms of Lucas Sequences Modulo $3^{k}$

J. C. Saunders, R. Nicholas Stephens

The Fibonacci sequence defined by $F_{0} = 0$ , $F_{1} = 1$ , and $F_{n} = F_{n - 1} + F_{n - 2}$ has a shortest period length of $4 \cdot 3^{k - 1}$ modulo $3^{k}$ for every $k \in N$ . In 2011, Bun…

math.NT2024

Runs of integers with constant values of the Carmichael function

Noah Lebowitz-Lockard, J. C. Saunders

In 2023, the first author and Vandehey proved that the largest $k$ for which the string of equalities $λ (n + 1) = λ (n + 2) = \dots = λ (n + k)$ holds for some $n \leq x$ , where $λ$ is the Carmi…

math.NT2018

Sieve Methods in Random Graph Theory

Yu-Ru Liu, J. C. Saunders

In this paper, we apply the Turan sieve and the simple sieve developed by R. Murty and the first author to study problems in random graph theory. In particular, we obtain upper and…

Residues of Terms of Lucas Sequences Modulo 3k

Runs of integers with constant values of the Carmichael function

Sieve Methods in Random Graph Theory

Residues of Terms of Lucas Sequences Modulo $3^{k}$