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Sums and products
Carl Pomerance
Dartmouth College
Friday, December 2nd, 2011
4:00 – 5:00 PM
Kalkin 003
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 arbitrarily large numbers N, can there be sets of N positive
integers where both the number of pairwise sums and pairwise products is less than N^{3/2}? No one
knows. 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 more than a multiple of 5. Can you do better?
ADA: Individuals requiring accommodations please contact Doreen Taylor at (802) 656-3166