Armstrong number

Given a base $b$ integer

$$n=\sum _{i=1}^k{d}_i{b}^{i-1}$$

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.

Title	Armstrong number
Canonical name	ArmstrongNumber
Date of creation	2013-03-22 16:04:06
Last modified on	2013-03-22 16:04:06
Owner	CompositeFan (12809)
Last modified by	CompositeFan (12809)
Numerical id	4
Author	CompositeFan (12809)
Entry type	Definition
Classification	msc 11A63
Synonym	narcissistic number
Synonym	plus perfect number
Synonym	perfect digital invariant