Difference between revisions of "2025 IMO Problems/Problem 4"
(Created page with "A proper divisor of a positive integer <math>N</math> is a positive divisor of <math>N</math> other than <math>N</math> itself. The infinite sequence <math>a_1,a_2,\dots</mat...") |
|||
| Line 1: | Line 1: | ||
| − | A proper divisor of a positive integer <math>N</math> is a positive divisor of <math>N</math> other than <math>N</math> itself. | + | A <i>proper divisor</i> of a positive integer <math>N</math> is a positive divisor of <math>N</math> other than <math>N</math> itself. |
The infinite sequence <math>a_1,a_2,\dots</math> consists of positive integers, each of which has at least three proper divisors. For each <math>n\ge1</math>, the integer <math>a_{n+1}</math> is the sum of the three largest proper divisors of <math>a_n</math>. | The infinite sequence <math>a_1,a_2,\dots</math> consists of positive integers, each of which has at least three proper divisors. For each <math>n\ge1</math>, the integer <math>a_{n+1}</math> is the sum of the three largest proper divisors of <math>a_n</math>. | ||
| Line 7: | Line 7: | ||
==Video Solution== | ==Video Solution== | ||
https://www.youtube.com/watch?v=Kb4h_GVFT1k | https://www.youtube.com/watch?v=Kb4h_GVFT1k | ||
| + | |||
| + | ==See Also== | ||
| + | * [[2025 IMO]] | ||
| + | * [[IMO Problems and Solutions, with authors]] | ||
| + | * [[Mathematics competitions resources]] | ||
| + | {{IMO box|year=2025|num-b=3|num-a=5}} | ||
Latest revision as of 19:52, 19 July 2025
A proper divisor of a positive integer 
is a positive divisor of other than itself.
The infinite sequence 
consists of positive integers, each of which has at least three proper divisors. For each 
, the integer 
is the sum of the three largest proper divisors of 
.
Determine all possible values of 
.
Video Solution
https://www.youtube.com/watch?v=Kb4h_GVFT1k
See Also
| 2025 IMO (Problems) • Resources | ||
| Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 5 |
| All IMO Problems and Solutions | ||
