I shall give you a hint on how to do this by brute force. There probably is a much more elegant way to do it, but elegance is not my strong suit.
All letters stand for integers.
[MATH]n \ | \ (3a + 7b) \text { MEANS } \exists \text { integer } q \text { s.t. } n * q = 3a + 7b.[/MATH]
[MATH]n \ | \ (2a + 5b) \text { MEANS } \exists \text { integer } p \text { s.t. } n * p = 2a + 5b.[/MATH]
From those two statements, can you show
[MATH]\therefore n \ | \ (3a + 7b), \text { and } n \ | \ (2a + 5b) \implies[/MATH]
[MATH]n \ | \ w(3a + 7b),\ n \ | \ w(2a + 5b), \text { and } n \ | \ \{u(3a + 7b) \pm v(2a + 5b)\}.[/MATH]
Those tools will allow you to demonstrate what you must demonstrate.