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 SSMO Relay Round 1 Problems

Revision as of 21:32, 15 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem 1== Compute the remainder when <math>2022^{2021^{2020^{\dots}}}</math> is divided by <math>2023</math>. Solution ==P...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem 1

Compute the remainder when $2022^{2021^{2020^{\dots}}}$ is divided by $2023$.

Solution

Problem 2

Let $T=$ TNYWR. Let $a_0 = 3, a_1 = 1, a_2 = N$, and let $a_n = a_{n-1} - \frac{a_{n-3}}{8}$. Find \[\sum_{i=0}^\infty a_i.\]

Solution

Problem 3

Let $T=$ TNYWR. Find the number of solutions to the equation \[ 

   \sec^{N} (Nx) - \tan^{N}(Nx) = 1

\] such $0 \le x \le \pi$ Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2023_SSMO_Relay_Round_1_Problems&oldid=207609"