Existence and Uniqueness Property On a Generalized Ledin-Brousseau Sum

In this paper, we present the existence and uniqueness property of the Ledin-Brousseau sum involving a polynomial and a homogeneous linear recurrence sequence. This sum is of the form k=1n P(k)shk+r, where n is a positive integer, P(x) is a polynomial in C[x], h and r are integers, and (sk)kZ is a homogeneous linear recurrence sequence of degree m 2 satisfying certain constraints.