# Strange Problem has me stumped

• September 23rd 2010, 02:24 AM
Carthage
Strange Problem has me stumped
Here is the question:
a, b and c are 3 different, positive integers, and (ab)^2 = abc.

Which of the following is a possible value for c?
1
5
9
12

I know the answer is 12, but i do not understand how to get this, aside from guess and check.
Any help would be appreciated.
• September 23rd 2010, 02:49 AM
Mollier
Hi,

since $(ab)^2 = abc$ then $c = ab$.

Can you multiply 2 different positive a and b to get, say 9 where neither a or b are 9?