Difference between revisions of "2016 AIME II Problems/Problem 8"
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Revision as of 20:21, 17 March 2016
Find the number of sets of three distinct positive integers with the property that the product of
and
is equal to the product of
.
Solution
Note that the prime factorization of the product is . Ignoring overcounting, by stars and bars there are
ways to choose how to distribute the factors of
, and
ways to distribute the factors of the other primes, so we have
ways. However, some sets have
numbers that are the same, namely the ones in the form
and
, which are each counted
times, and each other set is counted
times, so the desired answer is
.
Solution by Shaddoll