Mock AIME I 2015 Problems/Problem 9
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Since is a multiple of
, let
.
We can rewrite the first and second conditions as:
(a)
is a perfect square, or
is a perfect square.
(b)
is a power of
, so it follows that
,
, and
are all powers of
.
Now we use casework on
. Since
is a power of
,
is
or
or
.
If
, then no value of b makes
.