Mersenne: Factoring

[Eric Hahn]

  Does anybody know if there is an exponent where the
factor is, or know whether there is a proof on whether
a factor can (or can't) be, a root??  A square??

To clarify this: 
We know that any factor of 2^p-1 is in the form 2kp+1.
Letting x >=2, 
  Can (2kp+1)^x = 2^p-1 ??
  Can (2kp+1)^x * (2kp+1) ... = 2^p-1 ??

Eric Hahn


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