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Originally posted by EnlightenUp
Hmmm....quadratic formula + computer program? Seems simple enough. You are starting with coefficients and so the search is integer roots. Iterate through coefficients.
Edit:
Methinks I didn't understand your request fully so early in the AM. You want an algorthm that doesn't take O(N) but less time. Hmmm.
[edit on 10/28/2009 by EnlightenUp]
Originally posted by chiron613
I'm not sure I fully understand what you want. Do you mean you want some equation or formula that would allow you to enter your starting values (and perhaps -1 and 24 as well), that would immediately give you the ending values that are integers? If you do, then I'm not able to help you. I'm not sure there's a closed form for this process, and I'm not sure I'm up to finding it, even if there is one.
I'm curious to know what this is about, and why you are so certain that this process will always yield an integer value eventually. I'm also wondering what happens when your values wind up changing places - when your "smaller" number gets 24 added to it so many times that it becomes larger than the "larger" number. Then they swap places, back and forth...
Originally posted by Bass9
Does this have anything to do with solving the final piece to your "Prime Ray Theory", which by the way, was one of the best posts ever? I'm not a math genius although I do take great interest in it's applications. Good luck in your search. Just be sure that if you figure it out you don't steal my bank account...
Originally posted by EnlightenUp
Given the state of the unknowns, I am not holding out hope for a shortcut in general.
Check (b^2 - 4*a*c) is positive and a perfect square. Call this Z.
Check b +/- sqrt(Z) is even (both terms even or odd). Not much shortcut here though.
Originally posted by xmaddness
After a bit further thought, and some more coffee (I'm semi-conscious now)
Originally posted by EnlightenUp
reply to post by tauristercus
I made a small edit to my previous post with another possible check which would set a starting point.
But if either or both are NOT integer values, e.g. (23.76 and 57.9) ... or (237.2 and 673.58) ... or (76 and 142.62) then we modify the two starting numbers by adding 24 to the smaller of the two, and subtracting 1 from the larger of the two as shown here:
I'm curious to know what this is about, and why you are so certain that this process will always yield an integer value eventually. I'm also wondering what happens when your values wind up changing places - when your "smaller" number gets 24 added to it so many times that it becomes larger than the "larger" number. Then they swap places, back and forth...
Originally posted by xmaddness
reply to post by tauristercus
I see where my mistake was now.
But if either or both are NOT integer values, e.g. (23.76 and 57.9) ... or (237.2 and 673.58) ... or (76 and 142.62) then we modify the two starting numbers by adding 24 to the smaller of the two, and subtracting 1 from the larger of the two as shown here:
I saw the 23.76 number, and the fact that you added 24 to the smaller of the two, and assumed you were rounding the 23.76 up to the next number, 24, and adding that as a seed value for the next iteration.
I reread it and I see what you meant. I will put some more thought into this and see what I can come up with as far as a proof.
This may be a good candidate for proof by contradiction or contrapositive.