# Find the subgroup!

let p and q be distinct primes. suppose that H is a proper subset of integers and H is a group under addition that contains exactly 3 elements of the set
{ p,p+q,pq, p^q , q^p}.
Determine which of the foll are the 3 elements in H
a. pq, p^q, q^p

b. P+q, pq,p^q

c. p, p+q, pq

d. p, p^q, q^p

e. p, pq, p^q

matt grime
Homework Helper
Hint Euclid's algorithm: p^r and q^s are coprime so if H contains these two elements, then it contains 1, and hence is Z. Use this idea in several variations. Of course you could consider the group pZ

thanks sir, but could you please elaborate further.
i don't seem to get the idea...

matt grime
Homework Helper
If a group contains p, it contains np for all n in Z. So clearly e. forms the answer.

A group for instance cannot contain p and q if they are coprime and not be all of Z since there are a and b in Z such that ap+bq=1, hence the group contains all elements of Z.

And I tihnk you ought to ponder that for a while, cos I really have given you more information than I want to.

matt grime