Additive and Multiplicative Ramsey Theorems in N-Some Elementary Results

We show by elementary methods that given any finite partition of the set N of positive integers, there is one cell that is both additively and multiplicatively rich. In particular, this cell must contain a sequence and all of its finite sums, and another sequence and all of its finite products, a fact that was previously known only by utilizing the algebraic structure of the Stone-Cech compactification fiN of N.

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