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Old 2006-10-16, 16:22   #1
stpascu
 

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Default odd divisors of Mersenne-like, question

Could anyone help me with the following problem?

I have a conjecture that p is not a divisor for 2^p-1, for any odd integer p. It is known that if p is prime, then any divisor should be of the form 2kp+1 (Mersenne + Fermat), but I want to generalize and prove that p does not divide 2^p-1 for any odd p.

I found out recently about Mersenne primes, trying to solve this problem. It mostly resembles the type of answer I am looking for. I also thought that this forum is the most appropriate one. Any comments and/or suggestions would be appreciated. Thanks.

Stefan
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Old 2006-10-16, 16:31   #2
R.D. Silverman
 
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Nov 2003

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Quote:
Originally Posted by stpascu View Post
Could anyone help me with the following problem?

I have a conjecture that p is not a divisor for 2^p-1, for any odd integer p. It is known that if p is prime, then any divisor should be of the form 2kp+1 (Mersenne + Fermat), but I want to generalize and prove that p does not divide 2^p-1 for any odd p.

I found out recently about Mersenne primes, trying to solve this problem. It mostly resembles the type of answer I am looking for. I also thought that this forum is the most appropriate one. Any comments and/or suggestions would be appreciated. Thanks.

Stefan
Hint: If p is an odd composite, the 2^p-1 has algebraic factors.
What do you know about their divisors?
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