Difference between revisions of "2023 APMO Problems/Problem 2"
| Line 1: | Line 1: | ||
==Problem== | ==Problem== | ||
| − | Find all integers <math>n</math> satisfying <math>n \ge 2</math> and <math>\frac{\sigma(n)}{p(n)-1}</math>, in which <math>\sigma(n)</math> denotes the sum of all positive divisors of <math>n</math>, and <math>p(n)</math> denotes the largest prime divisor of <math>n</math>. | + | Find all integers <math>n</math> satisfying <math>n \ge 2</math> and <math>\frac{\sigma(n)}{p(n)-1}=n</math>, in which <math>\sigma(n)</math> denotes the sum of all positive divisors of <math>n</math>, and <math>p(n)</math> denotes the largest prime divisor of <math>n</math>. |
==Solution== | ==Solution== | ||
https://youtu.be/xkIm0k1FE-8 | https://youtu.be/xkIm0k1FE-8 | ||
Latest revision as of 20:51, 19 August 2023
Problem
Find all integers 
satisfying 
and 
, in which 
denotes the sum of all positive divisors of , and 
denotes the largest prime divisor of .
