Existence and Uniqueness Property On a Generalized Ledin-Brousseau Sum

Ivan Hadinata (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Gadjah Mada University, Yogyakarta)
Muhamad Abdillah Ahen (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Hasanuddin University, Makassar)

CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

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.