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 
.
