I need to find all integer solutions of the following equation:
$$2x + 3y + 4z = 5$$
So far I have already found, through a system of 2 equations in 2 variables, that one particular solution is $x = 15, y = -15,$ and $z = 5$.
There is a formula for finding all the integer solutions from two known solutions for two variables, I'm wondering if there is one for three? I imagine it would have to do with the gcd's of $2, 3$ and $4$.I just don't know quite what it would look like.
Thanks in advance!