# Linear Diophantine Equations

• December 8th 2008, 07:02 PM
mndi1105
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.
• December 8th 2008, 10:00 PM
CaptainBlack
Quote:

Originally Posted by mndi1105
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
• December 9th 2008, 11:30 AM
mndi1105
Yes, ax+by=c is the linear diophantine equation
• December 9th 2008, 11:31 AM
mndi1105
Sorry, also let (a,b)=1 and a,b,c positive integers