  The Hausdorff dimension of the set of simultaneously tau well approximable
points lying on a curve defined by a polynomial P(X)+alpha, where P(X) is a
polynomial with integer coefficients and alpha is in R, is studied when tau is
larger than the degree of P(X). This provides the first results related to the
computation of the Hausdorff dimension of the set of well approximable points
lying on a curve which is not defined by a polynomial with integer
coefficients. The proofs of the results also include the study of problems in
Diophantine approximation in the case where the numerators and the denominators
of the rational approximations are related by some congruential constraint.
