2016 AMC 10A Problems/Problem 25
Problem
How many ordered triples of positive integers satisfy
and
?
We prime factorize and
. The prime factorizations are
,
and
, respectively. Let
,
and
. We know that
and
since
isn't a multiple of 5. Since
we know that
. We also know that since
that
. So now some equations have become useless to us...let's take them out.
are the only two important ones left. We do casework on each now. If
then
or
. Similarly if
then
. Thus our answer is
.
See Also
2016 AMC 10A (Problems • Answer Key • Resources) | ||
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