Timeline for How many cubes are the sum of three positive cubes?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2023 at 18:37 | comment | added | LSpice | Re, $n \mapsto 1^3 + 1^3 + n^3$ is an injection from $\mathbb N_{> 0}$ to the set of sums of three positive cubes, so certainly there are infinitely many. | |
| Oct 9, 2023 at 17:40 | comment | added | user25406 | Thanks for the edit. I suspect there are an infinite number of numbers that are the sum of three positive cubes though I can't prove. Each equation which is based on $d=c+1$ produces two more equations for two different numbers besides the original. We have also $9-6$ and $9-1$ corresponding to $N=513$ and $N=728$. Beside, we can almost always ( of course no proof of that ) find a number by finding a solution involving some $c$ with $c=d-1,d-2,d-3....$ | |
| Oct 9, 2023 at 16:33 | comment | added | LSpice | This seems not to address "how many cubes are a sum of three positive cubes?", replacing it instead by "given a specific cube that we suspect is a sum of three positive cubes, what is a (more or less heuristic) method for finding them?" \\ Location-based references like 'above' do not work well on SO, when answers are in different positions on the page for different people, and at different times. I have edited in a reference to the answer that you seemed to mean. | |
| Oct 9, 2023 at 16:32 | history | edited | LSpice | CC BY-SA 4.0 |
Link to @Tomita's answer
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| Oct 9, 2023 at 16:09 | history | answered | user25406 | CC BY-SA 4.0 |