Sums and Products

Abstract

What could be simpler than to study sums and products of integers? Well maybe it is not so simple since there is a major unsolved problem: For any positive and arbitrarily large numbers N, is there a set of N positive integers where the number of pairwise sums is at most N2− and likewise, the number of pairwise products is at most N2−? Erdös and Szemerédi conjecture no. This talk is directed at another problem concerning sums and products, namely how dense can a set of positive integers be if it contains none of its pairwise sums and products? For example, take the numbers that are 2 or 3 mod 5, a set with density 2/5. Can you do better? This talk reports on recent joint work with P. Kurlberg and J.C. Lagarias. Sums and Products Carl Pomerance Dartmouth College FEATURED LECTURE BY: Marc-Thorsten Hütt