# Combinatorial number theory arising from algebraic topology.

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Don Davis , Lehigh University
Fine Hall 214

We will show how studying v1-periodic homotopy groups of SU(n) led to the following question. Let f(n) denote the sum of the reciprocals of the binomial coefficients (n choose i). For which p-adic integers x does the sequence f(x_n) approach a p-adic limit? Here x_n are the partial sums for x. The answer when p is odd is quite simple, but when p=2 is complicated and not completely understood.