Library / /32 of 60

, 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 $E$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; question papers published free at bmos.ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.