3 papers
math.NT2025
On denominators of consecutive -saturated Farey fractions
Jack Anderson, Florin P. Boca, Cristian Cobeli +1
The sequence of -saturated Farey fractions was defined in our previous work by ${\mathscr S}_Q := \{ a/q \in {\mathbb Q} \cap…
math.NT2025
On the distribution of -saturated Farey fractions
Jack Anderson, Florin P. Boca, Cristian Cobeli +1
We consider the set of Farey fractions of order with the property that there exists a matrix $\left( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix}…
math.NT2024
Arithmetic Polygons and Sums of Consecutive Squares
Jack Anderson, Amy Woodall, Alexandru Zaharescu
We introduce and study arithmetic polygons. We show that these arithmetic polygons are connected to triples of square pyramidal numbers. For every odd , we prove that there…