2014 AMC 12A Problems/Problem 14
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Problem
Let be three integers such that
is an arithmetic progression and
is a geometric progression. What is the smallest possible value of
?
Solution
We have , so
. Since
is geometric,
. Since
, we can't have
and thus
. then our arithmetic progression is
. Since
,
. The smallest possible value of
is
, or
.
(Solution by AwesomeToad)