Difference between revisions of "2003 AMC 10B Problems/Problem 18"
(Created page with "==Problem 18== What is the largest integer that is a divisor of <cmath> (n+1)(n+3)(n+5)(n+7)(n+9) </cmath> for all positive even integers <math>n</math>? <math>\textbf{(A) } 3 ...") |
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{{AMC10 box|year=2003|ab=B|num-b=17|num-a=19}} | {{AMC10 box|year=2003|ab=B|num-b=17|num-a=19}} | ||
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Revision as of 11:10, 4 July 2013
Problem 18
What is the largest integer that is a divisor of
![\[(n+1)(n+3)(n+5)(n+7)(n+9)\]](http://latex.artofproblemsolving.com/c/6/9/c694dd7f6739034188fe758646f1fd28508df784.png)
for all positive even integers 
?
Solution
Since the numbers being multiplied are all odd, 
is not a factor of the product, but 
and 
are since they are 5 consecutive odd numbers. This gives 
as the answer.
See Also
| 2003 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 17 |
Followed by Problem 19 | |
| 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 AMC 10 Problems and Solutions | ||
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