Let K be a field such that char(K) k and char(K) k + 1. We describe all (k + 1)-potent matrices over the group of upper triangular matrix. In the case that K is a finite field we show how to compute the number of these elements in triangular matrix groups and use this formula to compute the number of (k + 1)-potent elements in the Incidence Algebra I(X, K) where X is a finite poset.