The algebraic structure of the set of solutions to the Thue equation

Let Fn be a binary form with integral coefficients of degree n⩾2, let d denote the greatest common divisor of all non-zero coefficients of Fn, and let h⩾2 be an integer. We prove that if d=1 then the Thue equation (T) Fn(x,y)=h has relatively few solutions: if A is a subset of the set T(Fn,h) of all solutions to (T), with r:=card(A)⩾n+1, then(#)h divides the number Δ(A):=∏1⩽k