Kris Garrett writes:
Has it been proven that all mersenne numbers greater than one are
square free?
Depends on your definition of 'Mersenne numbers'. If you include
composite exponents, M(6) = 2^6 - 1 = 63 = 3*3*7 is not square free.
If you include only prime exponents, then you don't need to specify
"greater than one".:)
But, so far as I'm aware, there is no proof that all prime exponent
Mersenne numbers are square free. There is a partial proof towards
the end of my mersenne.html page.
Will
http://www.garlic.com/~wedgingt/mersenne.html
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