We consider solving for a and b the congruence a≡bh mod I, where a, b and h are (multivariable) polynomials and I is a polynomial ideal. This is a generalization of the well-known problem of Padé approximation of which decoding Hensel codes is a special case. We show how Gröbner bases of modules may be used to generalize the Euclidean algorithm method of solution of the 1-variable problem.
