Armstrong number

Given a base $b$ integer $$n = \sum_{i = 1}^k d_ib^{i - 1}$$ where $d_1$ is the least significant digit and $d_k$ is the most significant, if it's also the case that for some power $m$ the equality $$n = \sum_{i = 1}^k {d_i}^m$$ also holds, then $n$ is an Armstrong number or narcissistic number or plus perfect number or perfect digital invariant.

In any given base $b$ there is a finite amount of Armstrong numbers, since the inequality $k(b - 1)^m > b^{k - 1}$ is false after a certain threshold.