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Math Help - Prove by induction

  1. #1
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    Prove by induction

    .
    Last edited by watzer; March 4th 2010 at 10:33 AM.
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  2. #2
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    Quote Originally Posted by watzer View Post
    Hi! I'm stuck!

    How to prove that a equation x + y = n always have a positive solution(x,y >= 0) when n > z?


    What is z??

    "a Linear Diophantine equation"
    (Ex: 69x + 39y = n, when n > 20)


    This is false: any solution to this equation will have x or y negative if , for example, n = 21

    Tonio

    My steps have been:
    Solve the equation as u solve diofantic equations:
    so u get:
    Ex:
    x + y = 1 (in my case GCD(x,y) were one)

    then i did multiply all solutions with the value EX: 21,22,23,24,25 ( if n > 20 )

    and i got diffrent x,y values on all five wich had all one value of K were X,Y where positive.
    (ex:x = -110-49k, y = 155 + 69k)


    and all solutions over n > z had atleast one solution wich both x and y were positive.

    And then i got a pattern similar to this

    Ex:
    n 21---22----23---24----25
    X 50---52----54---56----58
    Y 100--105--110--115--120
    K 2-----2-----3-----3------4

    But have no idea how to prove it with induction.

    Is it posible to prove X then prove Y and by that K is proven to consist and always have a solution ?
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  3. #3
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    Yes true, diden't want to post my equation. But what if a equation have atleast one solution positive when n > 5(random number)

    How to prove it ?

    Prove the basestep: n = 6

    Prove n = p + 1


    Can u help me please, sorry for the lack of information on this.
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  4. #4
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    Quote Originally Posted by watzer View Post
    Yes true, diden't want to post my equation. But what if a equation have atleast one solution positive when n > 5(random number)

    How to prove it ?

    Prove the basestep: n = 6

    Prove n = p + 1


    Can u help me please, sorry for the lack of information on this.


    I can't help since I don't understand what you want...you must try harder to write your questions in a clear way.

    For example, if it MUST be that x,y>0 , then the two-inknown equation x+y=n has at least a positive solution (meaning that both x,y are positive) iff n\geq 2...but I'm not sure this is what you want.

    Tonio
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  5. #5
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    I want to prove for a diofantic equation (x + y = n, n > value) that there is always a value of K where x and y are non-negative. (>= 0)

    is it posible to prove that ?
    x: 5p+12k
    Y: -2p-5k

    will always have atleast a nonnegative solution when p > 43

    Do you have msn messenger ? So i can show you my calculations, PM me your messenger, i cant PM yet.
    Last edited by watzer; February 18th 2010 at 04:19 AM.
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  6. #6
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    Thumbs up

    Thanks for the help, think i have solved it.
    Last edited by watzer; February 18th 2010 at 01:10 PM.
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