Hi Codeforces, I have a problem where the solution is to solve diofant equation with K unknowns and K > 2. For example one equation of this type is: a1 * x + a2 * y + a3 * z = n and I have to find one solution of x, y and z. It is guaranteed that the equation always have a solution. Are there any algorithm that solve this problem? I will be thankful for helping :)
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Reduce it to the equation with 2 variables
A condition for a solution to exist: gcd(a1, a2, a3) divides n.
Now, if we rewrite the equation as: a1 * x + a2 * y = n - a3 * z, using the condition above, it shouldn't be hard to find z such that gcd(a1, a2) divides n - a3 * z. When you manage to do that, just solve the regular Diophantine equation left.