1987 AIME Problems/Problem 5
From AoPSWiki
Problem
Find 
if 
and 
are integers such that 
.
Solution
If we move the 
term to the left side, it is factorable:
is equal to 
. Since and are integers, 
cannot equal a multiple of three. 
doesn't work either, so 
, and 
. This leaves 
, so 
. Thus, 
.
See also
| 1987 AIME (Problems • Resources) | ||
| Preceded by Problem 4 | Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
