1989 AIME Problems/Problem 14
Problem
Given a positive integer 
, it can be shown that every complex number of the form 
, where 
and 
are integers, can be uniquely expressed in the base 
using the integers 
as digits. That is, the equation
is true for a unique choice of non-negative integer 
and digits 
chosen from the set 
, with $a_m\ne 0^{}^{}$ (Error compiling LaTeX. Unknown error_msg). We write
to denote the base expansion of . There are only finitely many integers 
that have four-digit expansions
Find the sum of all such 
.
Solution
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