This week's meeting of the Temple Math Club will feature a talk by Professor Charles Osborne on a proof the Sylvester-Schur Theorem. And, of course, there will be free pizza!
Abstract: In this talk, we will go over an elementary proof of the Sylvester-Schur Theorem, which states that if k and x are positive integers, and x>k, then at least one of the numbers x, x+1, x+2, x+3, … , x+(k-1) admits a prime divisor which is greater than k. The result was first discovered by James J. Sylvester in 1892 and rediscovered by Issai Schur in 1929. The proof we consider here is due to Paul Erdos, and has few prerequisites besides some basic properties of binomial coefficients, especially central binomial coefficients. This theorem may be viewed as a generalization of Bertrand’s Postulate.