Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Brian Nakamura**, Rutgers University, bnaka {at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Automated symbolic number theory

Speaker: **Eric Rowland**, UQAM

Date: Thursday, April 5, 2012 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

In the last several decades symbolic algebra has been developed extensively, to the point that modern software is capable of routinely manipulating sums, integrals, and so on.
So far, however, not much attention has been paid to expressions involving basic number theoretic functions such as mod(*n*, *k*) (the least nonnegative integer congruent to *n* modulo *k*) and ν_{k}(*n*) (the exponent of the highest power of *k* dividing *n*).
An implementation of basic properties of these functions goes a long way, and for example can perform automated case analyses on expressions involving them, giving automated proofs of identities which are tedious and not enlightening to prove by hand.
The particular motivation was to automate part of a proof, with Jeff Shallit, that the lexicographically least 3/2-power-free word on the nonnegative integers is a 6-regular sequence.
However, the tools are applicable in a number of other settings.