Abstract :
This paper is concerned with equations αx = R(x, y) in unknowns x, y set membership, variant image. Here α is a nonzero complex number which is not a root of 1, and R is a rational function with complex coefficients and an expansion R(X, Y) = r0Yl + r1(X) Yl − 1 + · · · where r0 is a nonzero constant. We will show that there are at most finitely many solutions unless α and R are of a very special form.
