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Old 2011-03-04, 16:16   #12
R.D. Silverman
 
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"Bob Silverman"
Nov 2003
North of Boston

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Quote:
Originally Posted by R.D. Silverman View Post
You just changed your original statement.

Your original statement was that x^n = x is not true when n = 2^p-1
is composite. Here x = 2^a + 2^b for a!= b

This is different from x^{n-1} = 1 is not true when n = 2^p-1 is
composite.
Note that 34 = 2^1 + 2^5 and 34^255 = 34 mod 255. Enough said?

Not enough? Note that 65 = 2^0 + 2^6 and 65^510 = 1 mod 511.

Still not enough? 72 = 2^3 + 2^6 and 72^510 = 1 mod 511.

I am sure that one could find additional counter-examples.

There was no reason to believe that an integer with Hamming weight 2
could not be a false witness to Mersenne numbers.
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