Nicely done.
Course: Foundations of Higher Mathematics
Prove that if and only if
I feel confident about this one. It's only the first part of the biconditional. Here's my attempt.
Assume that , i.e. , for some integer a.
Then,
.
Since is an integer, b is an integer also.
Therefore is odd, which means that is odd, i.e. , for some integer c.
Then,
, for some integer d
Therefore , hence