2000 AIME I Problems/Problem 11
From AoPSWiki
Problem
Let 
be the sum of all numbers of the form 
where 
and 
are relatively prime positive divisors of 
What is the greatest integer that does not exceed 
?
Solution
Since all divisors of 
can be written in the form of 
, it follows that 
can also be expressed in the form of 
, where 
. Thus every number in the form of 
will be expressed one time in the product
Using the formula for a geometric series, this reduces to 
, and 
.
See also
| 2000 AIME I (Problems • Resources) | ||
| Preceded by Problem 10 | Followed by Problem 12 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
