On a Conjecture of R. J. Simpson About Exact Covering Congruences

By Doron Zeilberger

A much shorter version

appeared in: Amer. Math. Soc. 96 (1989), 243.

R. Jamie Simpson killed (i.e. found a counter-example to) a conjecture of S. Znam, but tried to make up for it by posing a modified conjecture. In this short note, I use the powerful Berger-Felzenbaum-Fraenkel method to "kill" Jamie's conjecture. This reminded Aviezri Fraenkel of the words of the Sage Hillel who said (to a corpse of a drowned man): "because you have drowned others, you were drowned, and your drowners shall be drowned in their turn". Hence I did not even try to make up a new conjecture.

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