(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Proving stuff is a Subgroup

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