>>5
Since there's a '2008' in there, it's from some competition. It's not from the AIME, USAMO, or IMO, and the Putnam hasn't happened yet, so it's either from some small american competition, in which case is should be easy, or a foreign test, which seems more likely since OP seems to have a weak grasp on english. I can't find it, though.
Man this question would have been a lot easier last year.
Name:
Anonymous2008-11-22 10:09
Yes. A0 is 1, B0 is 3. That would make (A0+B0)/2 = 2. I'll call the third one C0. The product of A0, B0, and C0 is 6. This is obviously a factor of 6^2008. So, if we multiply each number by 6^(2007/3) or 6^669, we get A = 6^669, C = 2*6^669, and B = 3*6^669, which would give a product of 6^2008.