Date of Award
Summer 2025
Document Type
Open Access Dissertation
Department
Mathematics
First Advisor
Michael Filaseta
Abstract
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 reciprocals of the moduli in the covering system is bounded away from 1. In 1973, P.~Erd\H os and J.~Selfridge indicated that they believed that $m_0$ > 4 would suffice. We provide a proof that this is the case in Chapter 2. Chapters 3 and 4 are dedicated to showing that $0,1$-polynomials of high degree and few terms are irreducible with high probability. Formally, let $k\in\mathbb{N}$ and $F(x)=1+\sum_{i=1}^kx^{n_i}$, where $ 0
Rights
© 2025, Alexandros Kalogirou
Recommended Citation
Kalogirou, A.(2025). On a Conjecture on Covering Systems and an Irreducibility Question on Sparse 0,1-Polynomials. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/8525