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Starting from Ritt's classical theorems, we give a survey of results infunctional decomposition of polynomials and of applications in Diophantineequations. This includes sufficient conditions for the indecomposability ofpolynomials, the study of decompositions of lacunary polynomials and thefiniteness criterion for the equations of type f(x) = g(y).

Functional composition of polynomials: indecomposability, Diophantine equations and lacunary polynomials