# Math Help - Linear Diophantine Equations

1. ## 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.

2. 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

3. Yes, ax+by=c is the linear diophantine equation

4. Sorry, also let (a,b)=1 and a,b,c positive integers