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Math Help - Linear Diophantine Equations

  1. #1
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    Linear Diophantine Equations

    Prove that there are exactly ((a-1)(b-1))/2 values of c with c< ab-a-b for which the equation has a solution in nonnegative integers x and y.
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  2. #2
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    Quote Originally Posted by mndi1105 View Post
    Prove that there are exactly ((a-1)(b-1))/2 values of c with c< ab-a-b for which the equation has a solution in nonnegative integers x and y.
    Are we supposed to knoe that the equation in question is:

    ax+by=c ?

    CB
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  3. #3
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    Yes, ax+by=c is the linear diophantine equation
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  4. #4
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    Sorry, also let (a,b)=1 and a,b,c positive integers
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