Moscow-Petersburg seminar on low-dimensional mathematics
Friday, June 18, 2004

Yu.Bilu (Bordeaux)
Diophantine equations with separated variables

We describe pairs (f,g) of polynomials with rational coefficients such 
that the equation f(x)=g(y) has infinitely many solutions in integers 
x,y. Using classical results of Siegel and Ritt, together with some 
ideas of M. Fried, we show that, up to a linear change of variables, any 
such pair is of the form f(x) = h(u(x)) and g(y) = h(v(y)), where u,v 
are polynomials of very particular form and h is an arbitrary polynomial 
with rational coefficients.

A joint work with Robert Tichy.

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