lunes, 11 de marzo de 2013

Apuntes para una historia del problema de los NPI

«... In 1985, a high school senior in Hawaii named David Williamson, who was taking mathematics courses at the University of Honolulu, proved that if an odd perfect number exists, it must have exactly one prime factor that, when divided by 4, leaves a remainder of 1. Williamson's professor didn't know whether the result was original and suggested he write to the legendary Erdös, who had just come through town. Williamson eventually got a letter back from Erdös: 'The result you proved is in fact due to Euler. He also proved that every even perfect number is of the form 2p-1(2p-1) where 2p-1 is a prime. It is also known (proved by Carl Pomerance) that an odd perfect number if it exists must have at least 7 distinct prime factors. Perhaps the following problem of mine will interest you...' Williamson, now a combinatorialist at IBM, was thrilled. 'This letter to a high school student won't rank very high on Erdös's list of accomplishments, but it did mean a lot to me.'»

Paul Hoffman, The man who loved only numbers: the story of Paul Erdös and the search for mathematical truth. Hyperion, NY, 1998, pp. 47-48.

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