One of the most eccentric figures in the history of Mathematics was the Hungarian, Paul Erdös. He possessed the unique distinction of being by far the most published Mathematician (and with the most number of co-authors). He was famous as an itinerant sage that had no home but the halls of the Mathematics departments around the world. Erdös’ first paper included an elementary proof of Bertrand’s Postulate that states that between any positive number and its double there always lies a prime. This was to be but one of his many contributions to the field of number theory. Another field that Erdös propelled to great heights is that of Graph Theory. In particular, a question that he found entertaining in the last year of his life was that of edge magic labelings of graphs, an extension of the magic squares that have fascinated people since the ancient Chinese discovered the Lo-Shu (the 3 by 3 magic square).
In this talk the author presents some simple results on new concepts inspired by magic labelings, namely product magical labelings. The proofs of most of the results rely on Bertrand’s Postulate, a fact that thrilled the presenter and his co-authors as we started our journey down a research path inspired by Erdös’ interest in the topic and wound up using the first of his achievements to resolve our quandaries.
Click here for a biography of Joseph Bertrand
Click here for a biography of Pafnuty Chebyshev
Click here for a biography of Paul Erdös
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Page updated: Wednesday, October 1, 2003 9:00 AM HST