Xin-hua He

Refuting a Conjecture of Umans and Wang on Arithmetic-Progression Divisor Covers

An \emph{$n$-divisor set} is a finite set of positive integers containing a multiple of every integer from $1$ through $n$. Umans and Wang proposed, as the arithmetic-progression version of their Strong $(\alpha,\beta)$-Divisor Conjecture, an $n$-divisor arithmetic progression having at most $n^{2\beta}$ terms, each of...