Sloane's A046459 has an article on Dudeney numbers, which are integers equal to sum of the digits of their cubes.
For example: 18
3=5832, and 5+8+3+2=18. Accordingly, 18 is a Dudeney number.
The said article lists 0,1,8,18,26, and 27 as all possible Dudeney numbers.
A Dudezero number is a base 10 nonnegative integer the digits of whose cubes are each reduced by 1 and the said integer is equal to the sum of transformed digits.
For example, 5 is a Dudezero number, since:
5
3=125, and:
(1-1)+(2-1)+(5-1)=5
Determine all possible Dudezero numbers.
Absolutely, based on the information you provided, it appears that there are no Dudezero numbers.
Here's why:
The definition of a Dudezero number states that the sum of the digits of its cube, minus one for each digit, must equal the original number. The process of cubing a number and then subtracting one from each digit significantly increases the value. For instance, even a small single-digit number cubed will result in a much larger number after subtracting one from each
https://flashessay.com/ digit.
Since Dudezero numbers are restricted to non-negative integers, it becomes impossible to find a number whose digit sum, after being reduced by one, remains less than or equal to the original number. This effectively eliminates the possibility of any Dudezero numbers existing.
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