chapter  5
3 Sums of Arbitrary Limits
Pages 2

For the cases when there are no roots in the interval [0, n), the obvious idea is to sum the products. To deal with other cases, suppose we have two integral roots, say α and β, satisfying

0 ≤ α < β < n, and that we have one of the two cases

t((α, β), n, k) =

{ [β − k]β−α, [k − α− 1]β−α.