BMO Round 1, 2021

Number theory Difficulty 5.0 AIME, harder Find the answer United Kingdom

In the equation
$A^{AA} + AA = B,BBC,DED,BEE,BBB,BBE$
the letters $A$ , $B$ , $C$ , $D$ and $E$ represent different base 10 digits (so the right hand side is a sixteen digit number and $AA$ is a two digit number). Given that $C = 9$ , find $A$ , $B$ , $D$ and $E$ .

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