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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- Dec 8th 2008, 07:02 PMmndi1105Linear 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.

- Dec 8th 2008, 10:00 PMCaptainBlack
- Dec 9th 2008, 11:30 AMmndi1105
Yes, ax+by=c is the linear diophantine equation

- Dec 9th 2008, 11:31 AMmndi1105
Sorry, also let (a,b)=1 and a,b,c positive integers