Abstract:
Markov's equation is the Diophantine equation
$$
x^2+y^2+z^2=3xyz.
$$
It was first considered by A. A. Markov in connection with the theory of
integer quadratic forms and diophantine approximations.
Later it turned out that solutions to the Markov equation suddenly appear in
various, far from each other areas of mathematics. The talk will
be devoted to an overview
of solved and open problems related to the Markov equation and its
generalizations.
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