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Repunit Rigor (Posted on 2011-10-25) Difficulty: 4 of 5
Can any base ten repunit, other than 1, be a perfect cube?

If so, give an example. Otherwise prove that no base ten repunit (other than 1) can be a perfect cube.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (2 votes)

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Some Thoughts Wow... Is this really a D4? (spoiler--based on Google search) | Comment 2 of 5 |

Googling "repunit cube" results in most references saying that it is not known if there are any repunits that are cubes. A couple seem to disagree and quote a single source, and claim that there are no repunit perfect cubes. They don't show the proof, only point to, as I said, a single reference.

In any case, it would seem as difficult as solving the Riemann Hypothesis or Goldbach conjecture (at least a D5).

  Posted by Charlie on 2011-10-25 12:38:22
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