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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.