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.
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.
# posted by James Harris @ 16:53 
