I have these diophantine equations:

- x(m + 2y) = n
- x(m + 3y) = n

where m and n are *some* integers. How do I check if solutions exist for these equations (where x and y are integers)?

Note:

- I don’t need the solutions. I just need to determine if solutions exist.
- This is
**NOT**a system of equations. These are unique equations.

I thought of using Bezout’s lemma but I couldn’t apply it.