SUMS OF TERMS OF RECURRENCE SEQUENCES AND S -UNITS IN THE SOLUTION SETS OF NORM FORM EQUATIONS

Abstract We prove two results related to the solutions of norm form equations. First, we give a finiteness result for sums of terms of linear recurrence sequences appearing in the coordinates of solutions of norm form equations. Second, we give a finiteness result concerning solutions of norm form equations representable as sums of S -units with a fixed number of terms. To prove these results, we use a deep result concerning the finiteness of the solutions of polynomial-exponential equations and S -unit equations.