Difference between revisions of "2003 AIME I Problems/Problem 1"
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where <math> k </math> and <math> n </math> are [[positive integer]]s and <math> n </math> is as large as possible, find <math> k + n. </math> | where <math> k </math> and <math> n </math> are [[positive integer]]s and <math> n </math> is as large as possible, find <math> k + n. </math> | ||
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==Solution 2 (Alcumus)== | ==Solution 2 (Alcumus)== | ||
Revision as of 07:26, 21 November 2023
Problem
Given that
where 
and 
are positive integers and is as large as possible, find 
Solution 2 (Alcumus)
Note that![\[{{\left((3!)!\right)!}\over{3!}}= {{(6!)!}\over{6}}={{720!}\over6}={{720\cdot719!}\over6}=120\cdot719!.\]](http://latex.artofproblemsolving.com/8/6/8/868eddc32a5e4c6b77ab9b1510ff91597ff430c9.png)
Because 
, conclude that must be less than 720, so the maximum value of is 719. The requested value of 
is therefore 
.
~yofro
See also
| 2003 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
