Notes on Denumerants

A Characteristic Equation. If n, a₁,..., a_r are given integers, n ≥ 0, a₁ > 0, . . . , a_r > 0, the number of sets (x₁, ..., x_r) of integers x₁ ≥ 0,........, x_r ≥ 0 such that

a₁x₁+........+a_rx_r = n.