What? n is an integer multiple of b so n must divide b? 6 is an integer multiple of 3 but 6 does not divide three! You want to show that b is an integer multiple of n. In any case, alone does NOT show that "this is an integer multiple of b". Some factors of u+ vkb may cancel factors of b.

Is this right?

I'm also having trouble with the converse of the statement as well. I'll post any progress I make.