[Appeared in Elec. J. Combinatorics 8(2) (2001) (Special volume in honor of Aviezri Fraenkel), A1]

Dedicated to AVIEZRI FRAENKEL, on his 70th Birthday

Way back in the (early) eighties when I was in my (early) thirties, I have spent countless hours trying to find an elementary proof to the famous a_n=a_n-1 theorem about Covering Systems, begged by Erdos in many talks, all over the globe. I failed. Hence I could especially appreciate the BEAUTIFUL proof described in this article. I was so excited about this proof, that I described it, as a ten-minute digression, in many of my talks on unrelated subjects. Plus it was the center-piece of my talk in 1996, at the Tianjin Combinatorics meeting organized by Bill Chen. All these years I was hoping to write an expository paper about it, but never found the time. Luckily, Ed Scheinerman and Jamie Simpson asked me to contribute to the Fraenkel Festschrift that they are editing. So I finally decided that it is a great opportunity to finally realize my dream and at the same time pay homage to my great Rebbe, Aviezri Fraenkel.

P.S. This Birthday present is a bit late. Aviezri was born on June 7, 1929 (according to Who is Who in Israel)

Sasha, as I knew him, was about my age and I am now 74. His father was a cellist with the Moscow Orchestra, was branded a "dissident" and exiled to Siberia. Sasha and his mother immigrated to Israel during detent, and I met them there. We bonded, played chess and he came to the USA to study at Northwestern, and then Emory in Atlanta. In the early 1990's, he called me from Atlanta and said he needed to come see me. He took a train from Atlanta to New Orleans and told me he had a bicycle accident, had surgery and that the KGB had planted a device in his brain. The next day I took him to the Jewish Family Service in New Orleans and a social worker concluded he was suffering from paranoid schizophrenia and referred him to a service in Atlanta. That's the last I heard from him.

A Rutgers professor contacted afterwards (I don't remember who or know where he got my name) and told me about the publication that received some acclaim and was trying to reach him. Sadly, that was the end of the story. He was brilliant as only his colleagues would know, he had a warm heart, and a tortured life. Very sad.

Photo of Alexander Felzenbaum (ca. 1990, Courtesy of Michael Botnick)

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