Difference between revisions of "2005 AMC 10A Problems/Problem 21"
(merge) |
|||
Line 19: | Line 19: | ||
[[Category:Introductory Number Theory Problems]] | [[Category:Introductory Number Theory Problems]] | ||
+ | {{MAA Notice}} |
Revision as of 10:30, 4 July 2013
Problem
For how many positive integers does evenly divide from ?
Solution
If evenly divides , then is an integer.
Since we may substitute the RHS in the above fraction. So the problem asks us for how many positive integers is an integer, or equivalently when for a positive integer .
is an integer when is a factor of .
The factors of are , , , , , and , so the possible values of are , , , , , and .
But isn't a positive integer, so only , , , , and are possible values of . Therefore the number of possible values of is .
See also
2005 AMC 10A (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 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.