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?
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?
If $\displaystyle \gcd(a,b,c)=1$ it has solution.
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).2) What would be a general method of finding a solution if one exists?