# 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 ArmstrongNumber 2013-03-22 16:04:06 2013-03-22 16:04:06 CompositeFan (12809) CompositeFan (12809) 4 CompositeFan (12809) Definition msc 11A63 narcissistic number plus perfect number perfect digital invariant