[FONT=Verdana]Hi,
[FONT=Verdana]For any odd composite 'N', let u = (N-1)/2, v = u+1, then u^2(mod p) = v^2(mod p) if and only if 'p' is a factor of 'N'.
Hi,
For any odd composite 'N', let u = (N-1)/2, v = u+1, then u^2(mod p) = v^2(mod p) if and only if 'p' is a factor of 'N'.
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The logic that odd composite with least difference will be factored easily and large difference would factored hardly is wrong. B'coz whatever be the difference between the factors their exist Best Fermat Factors to make the Fermat factorization easier. Please follow the link to know more...