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Division (Posted on 2004-12-11) Difficulty: 3 of 5
For which positive integer values of N is 2^N-1 a multiple of N?

See The Solution Submitted by e.g.    
Rating: 3.8333 (6 votes)

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A Guess | Comment 1 of 16


So far I'm just starting on this, and I'm suspecting that there is no N>1. 

If there is such an N, then it must be true that:
2^N - 1 = k*N   where k is an integer

Also, 2^N - 1 in binary is a series of N 1's, which suggests that
2^N - 1  is divisible by 2^m - 1  if N is divisible by m
Not sure if this helps.

Now I'll pause and wait for someone else to present an elegant proof.

  Posted by Larry on 2004-12-11 17:03:14
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