On Wednesday, August 6, 2014 8:14:04 AM UTC-4, bert wrote: > On Wednesday, 6 August 2014 06:14:29 UTC+1, djoyce099 wrote: > . . . if it is there must be something in the E.C.M. algorithm > that recognize simple ratios between factors. That might be "Fermat factorization". You should Google it, and (just a polite suggestion, really) you should think about the impression you have created by posting such huge volumes of stuff, such egotism, and such disparaging remarks, while you were still ignorant of such an elementary and relevant 400-year old result. --
Not Fermat. Lehman's Algorithm. (and variations).
If N = pq and (p/q) is VERY close to the ratio of two small integers then N is trivially factored. This extends to (say) (p/q)^(d) for rational d of small height.
Perhaps if the OP were to actually READ about this subject, he might be able to talk about it without being totally clueless.
He still fails to provide the information that I told him was necessary to back his claim regarding the so-called ECM factorizations.
As it is, his posts are "not even wrong". They are nonsensical gibberish.