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Diophantine $m$-tuples

Florian Luca
Universidad Nacional Aut\'onoma de M\'exico

Thursday, May 12, 2005
L02 Carson Hall, 4 pm
Tea 3:30 pm, Math Lounge

Abstract: Let n be a nonzero integer. A set with the property D(n) is a set of m nonzero integers such that each pairwise product is n less than a square. What is of interest in general is to find upper bounds on m, the size of a set with the property D(n). In my talk, I will survey various known results about this problem and report on a few new ones. For example, one of the new results is that if n is a prime, then m<3\cdot 2^{144}. This work is joint with Andrej Dujella.

This talk will be accessible to graduate students.