1. The problem statement, all variables and given/known data Let a and b be integers (a) Prove that aZ + bZ is a subgroup of Z+ (b) prove that a and b+7a generate aZ + bZ 2. Relevant equations Z is the set of all integers 3. The attempt at a solution (a) In order for something to be a subgroup it must satisfy the following 3 properties: (i)closure; that is that if aZ and bZ are in H (the subgroup of Z+) than aZ+bZ are in H. (ii) identity: 0 is in H (iii) inverses: if a(Z)+ b(Z) are in H, then so are -(a(Z) + b(Z) i really dont know how to prove any of these are true for this particular subset. I am also completley lost on part b.