Difference between revisions of "1989 AIME Problems/Problem 14"
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Revision as of 07:50, 15 October 2007
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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See also
| 1989 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
