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Dudeney number - mklabgr - 07-06-2026
Dudeney number
Summary
A Dudeney number is a rare type of number with a surprisingly elegant property: it is a perfect cube whose digits add up to its cube root. For example, ($512 = 8^3$), and ($5 + 1 + 2 = 8$), making 512 a Dudeney number. The concept is named after the English puzzle creator Henry Dudeney, who introduced it in one of his famous recreational mathematics puzzles.
In the familiar decimal system, there are exactly six Dudeney numbers: $1, 512, 4913, 5832, 17576,$ and $19683$. The article also explains that mathematicians have generalized the idea to other number bases and powers, showing that although similar numbers exist in different settings, there are always only finitely many for any fixed base and exponent.
Dudeney numbers beautifully illustrate how simple operations like taking a cube and summing digits can combine to produce rare and fascinating patterns in number theory, making them a favorite topic in recreational mathematics.
ARTICLE