Armstrong number

Given a base b integer


where d1 is the least significant digit and dk is the most significant, if it’s also the case that for some power m the equality


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>bk-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