I'm still not that brilliant at proving things and i'm having trouble with this lemma.Lemma: Let a and n be integers with hcf(a,n)=1. Then
n divides ab if and only if n divides b.
I started with
Suppose n divides ab
Combining both expressions gives: .
This is an integer multiple of b so n must divide b.
Is this right?
I'm also having trouble with the converse of the statement as well. I'll post any progress I make.