M. Filaseta

collaborators

4 papers

math.NT2025

On the irreducibility of the non-cyclotomic part of most 0,1-polynomials with few terms

Michael Filaseta, Alexandros Kalogirou

We provide an alternative exposition of a result due to Schinzel. Fix an integer $k \geq 2$ . For almost all choices of positive integers $n_{1} < \dots < n_{k}$ , we show that the p…

math.NT2024

On extreme values of $r_{3} (n)$ in arithmetic progressions

Michael Filaseta, Jonah Klein, Cihan Sabuncu

For a given integer $m$ and any residue $a (mod m)$ that can be written as a sum of 3 squares modulo $m$ , we show the existence of infinitely many integers $n \equiv a (mod m)$ s…

math.NT2024

On the distance between factorials and repunits

Michael Filaseta, Florian Luca

We show that if $n \geq n_{0}$ , $b \geq 2$ are integers, $p \geq 7$ is prime and $n! - (b^{p} - 1) / (b - 1) \geq 0$ , then $n! - (b^{p} - 1) / (b - 1) \geq 0.5 lo g lo g n / lo g lo g lo g n$ . Further results are obta…

math.NT2024

Covering systems with the sum of the reciprocals of the moduli close to $1$

Michael Filaseta, Alexandros Kalogirou

In 1952, H. Davenport posed the problem of determining a condition on the minimum modulus $m_{0}$ in a finite distinct covering system that would imply that the sum of the reciproc…

On the irreducibility of the non-cyclotomic part of most 0,1-polynomials with few terms

On extreme values of r3​(n) in arithmetic progressions

On the distance between factorials and repunits

Covering systems with the sum of the reciprocals of the moduli close to 1

On extreme values of $r_{3} (n)$ in arithmetic progressions

Covering systems with the sum of the reciprocals of the moduli close to $1$