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Old 2010-11-03, 16:30   #3
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Jul 2009

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Originally Posted by Mini-Geek View Post
Note that all primes above 3 are either 1 or 5 mod 6.

Another way to write 5 mod 6 is -1 mod 6. When p is odd, 2^p-1 is 1 mod 6.
If N is 1 mod 6, then there must be an even number of factors that are -1 mod 6 (because the factors mod 6 have to multiply to the number mod 6). As far as I can tell, this can't be used to make it easier to find factors.
well for the 1/-1 mod 8 as well if p=3 mod 8 as I've listed before k = 1,5,9,etc. for 7(-1) mod 8 and k=0,4,8,12,16 etc. for 1 mod 8, if p=5 mod 6 to get 1 mod 6 use k=0,3,6,9,etc. ? and for 5 mod 6 k= 1,4,7,etc. ? is so when do k match up for the given mod 8 and mod 6 such that they can equal a common thing number that can be a factor.
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