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8191 has a partner (Posted on 2018-07-26) Difficulty: 3 of 5
8191 is a more-than-two-digit repunit prime in two bases:
8191 = 111 in base 90 = 1111111111111 in base 2.

Find the only other number with this property.

No Solution Yet Submitted by Ady TZIDON    
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proof of uniqueness Comment 3 of 3 |
it turns out the proof that this are in fact the only two such numbers is as yet incomplete, at least according to this wiki and a google search on the conjecture did not turn up any more recent work other than expanding the search bounds.


https://en.wikipedia.org/wiki/Goormaghtigh_conjecture




  Posted by Daniel on 2018-07-27 07:19:07
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