Sunday, March 02, 2008


z constraint and factoring

One tidbit result that has come out of the research into the concept I call surrogate factoring has been a constraint on z, where

z^2 = y^2 + nT

which I consider something of a weak constraint though it is an absolute one in a key way I'll explain is

z = (1 + 2α^2)k/(2α)

where k is just some non-zero integer, so it just boils down to z must have 1 + 2=E1^2 as a factor for some non-zero α that is an integer, which I consider kind of interesting.

If z has 3 as a factor, then of course, α = 1, works easily and the k can easily be found that will satisfy, so maybe it'd be more interesting as fun math oddity when z is NOT divisible by 3, and you try to find what α will work.

Theory as to why it's true is kind of neat, though trivially easy, unless I missed something! I'm fairly certain the result is true.

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