# Difference between revisions of "AoPS Wiki talk:Problem of the Day/July 4, 2011"

## Solution

$3^x-3 \equiv 0 \mod 16 \Rightarrow 3^x \equiv 3 \mod 16$.

So $3^x$ cycles through 3,9,11,1 mod 16, $x = 1$ doesn't work so try $x = 5$ which works and we're done.