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 Speed Round Problems/Problem 7

Revision as of 11:10, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Positive integers <math>a</math> and <math>b</math> satisfy <math>63a = 40b</math>. The sum of all possible values of <math>\tfrac{\varphi(a)}{\varphi(b)}</math>...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Positive integers $a$ and $b$ satisfy $63a = 40b$. The sum of all possible values of $\tfrac{\varphi(a)}{\varphi(b)}$ is $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2025_SSMO_Speed_Round_Problems/Problem_7&oldid=260027"