2025 IMO Problems/Problem 4

Revision as of 03:18, 16 July 2025 by Renrenthehamster (talk | contribs) (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...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

A proper divisor of a positive integer $N$ is a positive divisor of $N$ other than $N$ itself.

The infinite sequence $a_1,a_2,\dots$ consists of positive integers, each of which has at least three proper divisors. For each $n\ge1$, the integer $a_{n+1}$ is the sum of the three largest proper divisors of $a_n$.

Determine all possible values of $a_1$.

Video Solution

https://www.youtube.com/watch?v=Kb4h_GVFT1k