5 citations · 11 across the 5 of their papers we have counts for
5 papers · 1 filter
A generalization of the practical numbers
Nicholas Schwab, Lola Thompson
A positive integer is practical if every can be written as a sum of distinct divisors of . One can generalize the concept of practical numbers by applying an arit…
Arithmetic functions at consecutive shifted primes
Paul Pollack, Lola Thompson
For each of the functions and every natural number , we show that there are infinitely many solutions to the inequalities $f(p_n-1) < f(p_{n+1}-1) < \dots…
Bounded gaps between primes in number fields and function fields
Abel Castillo, Chris Hall, Robert J. Lemke Oliver +2
The Hardy--Littlewood prime -tuples conjecture has long been thought to be completely unapproachable with current methods. While this sadly remains true, startling breakthroughs…
Variations on a question concerning the degrees of divisors of x^n-1
Lola Thompson
In this paper, we examine a natural question concerning the divisors of the polynomial x^n-1: "How often does x^n-1 have a divisor of every degree between 1 and n?" In a previous p…
On the degrees of divisors of T^n-1
Paul Pollack, Lola Thompson
Fix a field . In this paper, we study the sets $\D_F(n) \subset [0,n]$ defined by [\D_F(n):= {0 \leq m \leq n: T^n-1\text{has a divisor of degree in} F[T]}.] When $\D_F(n)$…