>2^(q-1) mod q = 1
>
>==comment== (q-1) is the number of integers less than q that is not a 
>factor of q plus the number 1
>
>Then, 2^(q-1) -1 = x * q where x is any positive integer
>
>If N = 2^(q-1) - 1 = x * q
>
>then, N is a number with all binary digits equal to 1 and the number of 
>digits is EVEN (q-1).
>
>and N is the LOWEST VALUE of MULTIPLE of q with all binary digits equal to 
>1 (very important!!!)

The last line in this chain of reasoning is false.  Take q = 23.  Yes, 2^22 
mod 23 = 1, but 22 is not the lowest power of 2 where this is the 
case.  2^11 mod 23 = 1, so 11 is the lowest power of 2 which is congruent 
to 1 mod 23.


Nick Glover: [EMAIL PROTECTED]
Computer Science, Clemson University
Homepage: http://hubcap.clemson.edu/~nglover/

"It's good to be open-minded, but not so open that your brains fall out." - 
Jacob Needleman


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