Re: Surrogate factoring, out of the box

From: Tim Peters (tim.one_at_comcast.net)
Date: 01/29/05 

Date: Sat, 29 Jan 2005 16:32:08 -0500

[JSH]
> Well I'll admit that I've been feeling a bit depressed the last couple
> of days, as I had calculations showing at least 50% success with a
> rational x, and then I checked thoroughly and found that my method gave
> a LOT of rational x's, and wasn't factoring with most of them.

On sci.math, Rick Decker gave a detailed sketch of a proof that every
non-zero rational x satisfies the equations (or at least the best he was
able to decipher them from your paper). Nora Baron reached the same
conclusion, but disagreed with algebraic details in Rick's sketch. I also
reached the same conclusion, via a related approach, and illustrated it with
a small, fully worked-out numeric example.

Of course it's possible that none of us were able to make sense of your
intent (sorry, your paper is unclear on many points). But if we were, it's
no surprise that most x wouldn't lead to a non-trivial factor, and
especially not as the smallest prime factor of M increases.