Difference between revisions of "1984 AHSME Problems/Problem 28"
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Latest revision as of 12:52, 5 July 2013
Problem
The number of distinct pairs of integers 
such that 
and 
is
Solution
We can simplify 
to 
. Therefore, the only solutions are 
such that 
and 
. The only solutions to this are 
. Each of these gives distinct pairs of , so there are 
pairs, 
.
See Also
| 1984 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 27 |
Followed by Problem 29 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
