Difference between revisions of "2002 IMO Problems/Problem 4"
(Created page with "Solution 1 Trivial by AM-GM (jk i'll add my solution later) ~PEKKA") |
|||
| (5 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
| − | + | Problem: | |
| + | Let <math>n>1</math> be an integer and let <math>1=d_{1}<d_{2}<d_{3} \cdots <d_{r}=n</math> be all of its positive divisors in increasing order. Show that | ||
| + | <cmath>d=d_1d_2+d_2d_3+ \cdots +d_{r-1}d_r <n^2</cmath> | ||
| − | + | ==Solution== | |
| + | {{solution}} | ||
| + | |||
| + | ==See Also== | ||
| − | + | {{IMO box|year=2002|num-b=3|num-a=5}} | |
Latest revision as of 14:35, 17 June 2024
Problem:
Let 
be an integer and let 
be all of its positive divisors in increasing order. Show that
![\[d=d_1d_2+d_2d_3+ \cdots +d_{r-1}d_r <n^2\]](http://latex.artofproblemsolving.com/8/e/2/8e201bb9274ec9bd46a38d9681bf1b22e42d24da.png)
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 2002 IMO (Problems) • Resources | ||
| Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 5 |
| All IMO Problems and Solutions | ||
