1. Let n be a positive integer,
(a) Find $(n, n + 1)$
(b) Find $(n, n + 2)$
2. Suppose m, n are integers such that $(m, n) = 1$
Prove that $(m+n, m-n) = 1$ or 2
3. Let m be a positive integer.
(a) Prove that $(3m+2, 5m+3) = 1$
(b) Find integers $(a, b, c, d)$ other than $(3, 2, 5, 3)$
such that $(am + b, cm + d) = 1$. Of course explain
why your choice works.
4. Let a, b be integers such that $(a, b) = 1$
Prove that $(a + 2b, 2a + b) = 1$