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

2022 SSMO Team Round Problems/Problem 4

Problem

Let $a_1=2,b_0=3, a_n=\left(a_{n-1}\right)^2,$ and $b_n=\left(b_{n-1}\right)^3.$ If $c_n=a_n+b_n,$ find the last two digits of $c_1+c_2+\dots+c_{2022}.$

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2022_SSMO_Team_Round_Problems/Problem_4&oldid=207309"