Diophantine equation on an example I do have one task here, that could be solved my guessing the numbers. But the seminars leader said, also Diophantine equation would lead to solution. Has anyone an idea how it works? And could you please show it to me on that example here?
The example:
The number $400$ shall be divided into $2$ summands, the first summand should be divisible through $7$ and the second summand should be divisible through $13$. Thank you for help!

7x + 13y = 400 and 7x = 400(mod 13) which reduces to x = 7(mod 13) and x = 7 + 13k.
Substituting this x into the original equation gives y = 27 - 7k.
The complete solution is x = 7 + 13k and y = 27 - 7k.
