J. Saunders

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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 $I^» (n + 1) = I^» (n + 2) = \dots = I^» (n + k)$ holds for some $n \leq x$ , where $I^»$ is the C…

Residues of Terms of Lucas Sequences Modulo 3k

Runs of integers with constant values of the Carmichael function

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