2013 Mock AIME I Problems/Problem 3
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Problem
Let 
be the greatest integer less than or equal to 
, and let 
. If 
, compute 
.
Solution
Notice that the radical conjugate of x is a positive integer from 0-1. Since the sum of powers of two radical conjugates is an integer, 
is just the conjugate of x to the 
power. Therefore, the desired expression is just 001.
