by Quelloquialism » Mon Apr 23, 2007 12:31 am
Factor 2004.
You get [unparseable or potentially dangerous latex formula]. Distribute the exponent, and you have [unparseable or potentially dangerous latex formula].
The number of positive integral divisors of an integer is the product of all prime exponents increased by one.
So, we are looking for solutions to the equation [unparseable or potentially dangerous latex formula], where a, b, and c are all integers between 0 and 2003, inclusive (the 2003 limit is because, clearly, no solutions are possible if all terms are at least 1 and one term is at least 2003), representing the exponents of 167, 2, and 3, respectively.
As we already determined, 2004 = [unparseable or potentially dangerous latex formula].
Then my elegance engine crashed and I brute-forced the possible values of a, b, and c on paper, though I'm sure there's a better way. My brain doesn't work.