By Anthony Zaleski and Doron Zeilberger
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First Written: Jan. 15, 2018
To appear in Mathematics Magazine [in a slightly "edited" version, but we prefer the original]
Bob Hough recently disproved a long-standing conjecture of Paul Erdos regarding covering systems. Inspired by his seminal paper, we describe analogs of covering systems to Boolean functions, and more generally, the problem of covering discrete hyper-boxes by non-parallel lower dimensional hyper-subboxes. We point out that very often primes are red herrings. This is definitely the case for covering system, and who knows, perhaps also for the Riemann Hypothesis.
Added Feb. 9, 2019: Read this interesting follow-up article by Manuel Kauers, Martina Seidl, and Doron Zeilberger.
Doron Zeilberger's Home Page
Anthony Zaleski's Home Page