# Math Help - Question on linear diophantine

1. ## Question on linear diophantine

I have 2 questions:

1) Under what conditions on a,b,c is it true that the following equation has a solution:

ax+by+cz = 1 (where 1 is the gcd(a,b,c)?

and

2) What would be a general method of finding a solution if one exists?

2. Originally Posted by clockingly
I have 2 questions:

1) Under what conditions on a,b,c is it true that the following equation has a solution:

ax+by+cz = 1 (where 1 is the gcd(a,b,c)?
If $\gcd(a,b,c)=1$ it has solution.

2) What would be a general method of finding a solution if one exists?
You can ignore one of the variables for now and work with the other two. Use the general approach to solving first order linear diophantine equations to get the general solution now extend to the third variable. (It is not so nice).