1987 AIME Problems/Problem 8
From AoPSWiki
Problem
What is the largest positive integer 
for which there is a unique integer 
such that 
?
Solution
Multiplying out all of the denominators, we get:
Since 
, 
. Also, 
, so 
. Thus, 
. is unique if it is within a maximum range of 
, so 
.
See also
| 1987 AIME (Problems • Resources) | ||
| Preceded by Problem 7 | Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
