Difference between revisions of "1985 AHSME Problems/Problem 21"
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Revision as of 12:01, 5 July 2013
Problem
How many integers 
satisfy the equation 
Solution
Notice that any power of 
is , so 
would give valid solutions.
Also, 
to an even power also gives , so we check 
However, 
gives an odd power of , so this is discarded. Finally, notice that anything to the 
power (except for 
, which is debatable) gives .
This doesn't make 
, so this is also valid.
Overall, our valid solutions are 
for a grand total of 
.
See Also
| 1985 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 20 |
Followed by Problem 22 | |
| 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. 
