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

2023 WSMO Team Round Problems/Problem 8

Problem

Let $f(x)=\sqrt{x-\sqrt{x-\sqrt{x-\ldots}}}.$ Find the modulo 1000 on the minimum integer $a$ such $f(f(f(f(f(a)))))$ is a positive integer.

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2023_WSMO_Team_Round_Problems/Problem_8&oldid=247899"