Difference between revisions of "1999 AMC 8 Problems/Problem 24"
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Revision as of 23:34, 4 July 2013
Problem
When 
is divided by 
, the remainder is
Solution
Note that the units digits of the powers of 9 have a pattern: 
,
,
,
, and so on. Since all natural numbers with the same last digit have the same remainder when divided by 5, the entire number doesn't matter, just the last digit. For even powers of 
, the number ends in a 
. Since the exponent is even, the final digit is . Note that all natural numbers that end in have a remainder of when divided by . So, our answer is 
.
See Also
| 1999 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
| 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 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
