Definition:Perfect Digital Invariant
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Definition
Let $n \in \Z_{>0}$ be a positive integer.
$n$ is a perfect digital invariant if and only if when expressed in decimal notation the $n$th powers of its digits add up to some positive integer $m$.
Examples of Perfect Digital Invariants
4150 is a Perfect Digital Invariant to $5$th Powers
$4150 = 4^5 + 1^5 + 5^5 + 0^5$
Also see
- Definition:Recurring Digital Invariant
- Definition:Pluperfect Digital Invariant
- Results about perfect digital invariants can be found here.
Sources
- Weisstein, Eric W. "Narcissistic Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NarcissisticNumber.html