105 citations · 304 across the 45 of their papers we have counts for
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The Erdős-Selfridge problem with square-free moduli
Paul Balister, Béla Bollobás, Robert Morris +2
A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of covering systems with distinct moduli was initiated by Erdős in…
On the Erdős Covering Problem: the density of the uncovered set
Paul Balister, Béla Bollobás, Robert Morris +2
Since their introduction by Erdős in 1950, covering systems (that is, finite collections of arithmetic progressions that cover the integers) have been extensively studied, and nume…
A note on Linnik's Theorem on quadratic non-residues
Paul Balister, Béla Bollobás, Jonathan D. Lee +2
We present a short, self-contained, and purely combinatorial proof of Linnik's theorem: for any there exists a constant such that for any , the…
The sharp threshold for making squares
Paul Balister, Béla Bollobás, Robert Morris
Consider a random sequence of integers, each chosen uniformly and independently from the set . Motivated by applications to factorisation algorithms such as Dixo…