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In a reply late last week concerning large values of x and x having many
prime factors I made the comment that even pairs might be factored out
by multiplying them and then finding a different way to factor the product.
I as assuming that the product of two primes would not produce a product
which in general could not be factored a different way. This seems to be
in error. So far the vast majority of cases I have looked at have failed.
This leaves the problem of large values of x which have many prime factors
that appear either two or more times in n. At this point I don't see a
way to use this relationship to further gain.
Any ideas would be greatly appreciated.
Side Note: I have lost the original post concerning this subject. I am
still working on a paper concerning the behaviour of the mod
function and would like to provide credit where credit is
due. If you are the original author or can provide the e-mail
address (please reply via e-mail) of the author it would be