1. The problem statement, all variables and given/known data Suppose that H is a subgroup of Z under addition and that H contains 2^50 and 3^50. What are the possibilities for H? 2. Relevant equations Relevant concepts are just the definitions for a group and subgroup. https://en.wikipedia.org/wiki/Group_(mathematics) https://en.wikipedia.org/wiki/Subgroup 3. The attempt at a solution The solution I was given is the following: But what I'm wondering about, and would appreciate an answer to, is the following: But the subgroup has operation "addition" so 2^50 = 50*2 = (2*5*5)*2, and 3^50 = 50*3 = (2*5*5)*3, so the possibilities for H are: H=Z, H=2Z, H=10Z, H=25Z, H=50Z. Or am I missing something?