I saw a lot of similar questions asked on this forum, however they were all mostly generalizing to variables a, b, c, d etc. or proofs. However would like to see an example of solving one rather than a proof.
Find all integer solutions to the following linear diophantine question with 4 variables: 2x1 + 5x2 + 4x3 + 3x4 = 5
So I know gcd of a, b, c, d is same as a, b, (c, d), do we use that fact here?
The gcd for (2, 5, 4, 3) = 1 here but how would this help find x1, x2, x3, x4.
In the 2-variable case, I know we can use the Euclidean Algorithm to solve it, does it work in this case too? Or do we brute force this?