Difference between revisions of "2017 AIME II Problems/Problem 6"
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Revision as of 11:35, 23 March 2017
Find the sum of all positive integers
such that
is an integer.
Manipulating the given expression,
. The expression under the radical must be an square number for the entire expression to be an integer, so
. Rearranging,
. By difference of squares,
. It is easy to check that those are all the factor pairs of 843. Considering each factor pair separately,
is found to be
and
. The two values of
that satisfy one of the equations are
and
. Summing these together, the answer is
.