GR9367 Q55

[danielkim116]

hi,

I am stuck on this quesiton and any help would be appreciated.
Here is a question:

55. Let p and q be distinct primes. There is a proper subgroup J of the additive group of integers which contains exactly three elements of the set {p, p+q, pq, p^q, q^p}. Which three elements are in J?

answer: {p, pq, p^q}

thank you so much inadvance!

[blitzer6266]

Any additive group of integers is in the form cZ (c- any integer, Z-the integers). p, pq, and p^q are p-multiples while p+q and q^p are not, so the first three are in pZ, while the other two aren't.