GR9367 Q55

Forum for the GRE subject test in mathematics.
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GR9367 Q55

Post by danielkim116 » Sun Apr 04, 2010 9:16 am


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!

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Joined: Sun Apr 04, 2010 1:08 pm

Re: GR9367 Q55

Post by blitzer6266 » Sun Apr 04, 2010 1:14 pm

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.

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