N equals the cube of the sum of its digits

  • Thread starter Thread starter myth_kill
  • Start date Start date
  • Tags Tags
    Cube Sum
Click For Summary
The discussion focuses on identifying natural numbers n that equal the cube of the sum of their digits. The proposed solutions include n = 0, 1, 512, 4913, 5832, 17576, and 19683, depending on whether zero is counted. It is noted that candidates for n must be perfect cubes, which significantly narrows the search. The upper limit for k is established at 54, beyond which the condition cannot be satisfied. The use of tools like Openoffice is suggested for conducting an exhaustive search to find valid numbers.
myth_kill
Messages
19
Reaction score
0
Find all natural numbers n such that n equals the cube of the sum of its digits.
 
Physics news on Phys.org
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.
 
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.
 
Last edited:

Thread 'Confusion about the Moyal-Weyl twist'

I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...
View full post »

Similar threads

MHB Symmetry Operations of a Cube: Geometric Descriptions and Matrix Representations
  • · Replies 31 ·
2
Replies
31
Views
3K
Undergrad What are the groups for NxNxN puzzle cubes called?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Sum of Numbers on Cube Faces to Equal 2004
  • · Replies 1 ·
Replies
1
Views
2K
MHB Finding 3-Digit Numbers with Sum of Digits Squared = 2
  • · Replies 7 ·
Replies
7
Views
2K
MHB Find the smallest positive integer N
  • · Replies 3 ·
Replies
3
Views
1K
MHB Evaluating $\iint\limits_{\sum} f \cdot d\sigma $ on Cube S
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Why is the dual of Z^n again Z^n ?
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Converting momentum sums to integrals in curved spacetime
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Seeking an intuition linking definitions of contravariant and covariant
  • · Replies 1 ·
Replies
1
Views
2K
Understanding the Force of Two Cubes
  • · Replies 1 ·
Replies
1
Views
1K