1995 AHSME Problems/Problem 29
Problem
For how many three-element sets of positive integers is it true that
?
Solution
. The number of ordered triples
with
is therefore
, since each prime dividing 2310 divides exactly one of
.
Three of these triples have two of equal (namely when one is 2310 and the other two are 1). So there are
with
distinct.
The number of sets of distinct integers such that
is therefore
(accounting for rearrangement), or
.