2001 Pan African MO Problems/Problem 5
Problem
Find the value of the sum:
where
denotes the greatest integer which does not exceed
.
Solution
First, note that for positive integers , the list of integers
where
is
. Thus, there are
values of
where
.
Additionally, note that and
. There are
values of
where
. Therefore, the value
.
By rewriting the above value as a summation, we can compute the value to be equal to
See Also
2001 Pan African MO (Problems) | ||
Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
All Pan African MO Problems and Solutions |