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Graduate Student Number Theory Learning Seminar

"The Markov Equation mod p"

George Hauser, Rutgers University

Location:  HILL 525
Date & time: Wednesday, 12 April 2017 at 3:15PM -


Time: 3:15 PM
Location: Hill 525
Abstract: The markov equation is the equation x^2+y^2+z^2=3xyz. All of its integer solutions are obtained from the solution (1,1,1) by repeated application of "Vieta moves" and permutations of the coordinates. However, it is an open problem whether every solution in Z/pZ comes from a solution in Z. In this we will discuss some basic properties of the Markov equation mod p, and some recent results of Bourgain, Gamburd, and Sarnak in the direction of proving this conjecture.

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