Pace P. Nielsen

activity

20042025

most citedOdd Perfect Numbers Have At Least Nine Distinct Prime Factors

17 citations · 56 across the 8 of their papers we have counts for

collaborators

10 papers

math.RA2025

Algebraization of infinite summation

Pace P. Nielsen

An algebraic framework in which to study infinite sums is proposed, complementing and augmenting the usual topological tools. The framework subsumes numerous examples in the litera…

math.NT2022

Prime factors of $Φ_{3} (x)$ of the same form

Cody S. Hansen, Pace P. Nielsen

We parameterize solutions to the equality $Φ_{3} (x) = Φ_{3} (a_{1}) Φ_{3} (a_{2}) \dots Φ_{3} (a_{n})$ when each $Φ_{3} (a_{i})$ is prime. Our focus is on the special cases when $n = 2, 3, 4$ , as this analysis…

math.GR2018★ 9 cited

Homogeneous length functions on groups

D. H. J. Polymath

A pseudo-length function defined on an arbitrary group $G = (G, \cdot, e, ()^{- 1})$ is a map $ℓ : G \to [0, + \infty)$ obeying $ℓ (e) = 0$ , the symmetry property $\ell(x^{-1}) = \e…

math.AC2017

Transfinitely valued Euclidean domains have arbitrary indecomposable order type

Chris J. Conidis, Pace P. Nielsen, Vandy Tombs

We prove that for every indecomposable ordinal there exists a (transfinitely valued) Euclidean domain whose minimal Euclidean norm is of that order type. Conversely, any such norm…

math.NT2017★ 11 cited

Covering systems with restricted divisibility

Robert D. Hough, Pace P. Nielsen

We prove that every distinct covering system has a modulus divisible by either 2 or 3.

math.RA2015

Connections between unit-regularity, regularity, cleanness, and strong cleanness of elements and rings

Pace P. Nielsen, Janez Šter

We construct an example of a unit-regular ring which is not strongly clean, answering an open question of Nicholson. We also characterize clean matrices with a zero column, and thi…