M. Filaseta

activity

20042026

most citedFactorization of polynomials in hyperbolic geometry and dynamics

1 citations · 2 across the 16 of their papers we have counts for

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17 papers · 1 filter

math.NT2026

On the factorization of $x^{d_{r}} + x^{d_{r - 1}} + \dots + x^{d_{2}} + x^{d_{1}} + p$ and a conjecture of C. Nicol

Michael Filaseta, Lilit Martirosyan, London Cameron Swan

For an arbitrary prime $p$ and arbitrary positive integers $r$ and $d_{1}, \dots, d_{r}$ with $d_{r} > \dots > d_{1}$ , we show that $x^{d_{r}} + x^{d_{r-1}} + \cdots + x^{d_{2}}…

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…

math.NT2023

A generalization of a fourth irreducibility theorem of I. Schur

Martha Allen, Michael Filaseta

Let $u_{2 j}$ be the product of the odd positive integers $< 2 j$ . For $n$ an integer $\geq 1$ , define \[ f(x)=\sum_{j=0}^{n}a_j\frac{x^{2j}}{u_{2j+2}}, \] where the $a_{j}$ 's are arbit…

On the factorization of xdr​+xdr−1​+⋯+xd2​+xd1​+p and a conjecture of C. Nicol

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

A generalization of a fourth irreducibility theorem of I. Schur

On the factorization of $x^{d_{r}} + x^{d_{r - 1}} + \dots + x^{d_{2}} + x^{d_{1}} + p$ and a conjecture of C. Nicol

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

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