Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2025 SSMO Team Round Problems/Problem 7

Revision as of 11:32, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>n</math> be the largest integer such that <math>20!^{25!} + 25!^{20!}</math> is divisible by <math>2025^n</math>. The value of <math>n</math> can be wri...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $n$ be the largest integer such that $20!^{25!} + 25!^{20!}$ is divisible by $2025^n$. The value of $n$ can be written in the form $a\cdot b!,$ where $a$ and $b$ are positive integers and $b$ is maximized. Find $a+b$.

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2025_SSMO_Team_Round_Problems/Problem_7&oldid=260059"