N equals the cube of the sum of its digits

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In summary, the conversation discusses finding all natural numbers n that equal the cube of the sum of their digits. The solution provided is n = 0, 1, 512, 4913, 5832, 17576, 19683, depending on whether or not zero is counted. The process of proving this is described, including using an exhaustive search with the help of Openoffice. The speaker also asks for feedback or comments on their solution.
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myth_kill
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Find all natural numbers n such that n equals the cube of the sum of its digits.
 
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If it were the sum of the individual cubes of the digits, then there is

1^3 +5^3 +3^3 =153

But I guess that's not the answer you require.
 
  • #3
I believe that there are 6 or 7 answers; n = 0, 1, 512, 4913, 5832, 17576, 19683. It depends if you are counting zero or not.

Proving this is another story. First, candidates for n must be equal to 'k' cubed. So we can eliminate a lot numbers with that statement. Once 'k' gets to be 54, (n = 157464), it is impossible for the sum of digits of n to be equal to its cube root (k). Thus one can perform an exhaustive search for k = 0..54 to find the only answers. Openoffice helps with the exhaustive search.

Am I missing something here? Any comments are appreciated.
 
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Related to N equals the cube of the sum of its digits

1. What is the meaning of "N equals the cube of the sum of its digits"?

This phrase refers to a mathematical equation where the value of N (a number) is equal to the cube of the sum of its individual digits. For example, if N is 123, then the sum of its digits (1+2+3) is 6, and the cube of 6 is 216, which is equal to N.

2. How does this equation relate to mathematics?

This equation falls under the branch of mathematics known as number theory, which deals with the properties and relationships of numbers. It involves concepts such as addition, multiplication, and exponents.

3. What is the significance of this equation?

This equation is interesting from a mathematical standpoint because it has been proven to always hold true for any positive integer. It also has practical applications in areas such as computer programming and cryptography.

4. Can this equation be used to find the roots of a number?

No, this equation cannot be used to find the roots of a number. Finding the roots of a number involves using a different mathematical process, such as taking square roots or using the quadratic formula.

5. Are there any real-life examples of this equation being used?

Yes, this equation has been used in the field of cryptography to create secure encryption algorithms. It has also been used in computer programming to generate unique identification numbers for objects or data. Additionally, it has been used in number games and puzzles as a fun mathematical concept.

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