Difference between revisions of "2023 SSMO Relay Round 1 Problems/Problem 1"
(Created page with "==Problem== Compute the remainder when <math>2022^{2021^{2020^{\dots}}}</math> is divided by <math>2023</math>. ==Solution==") |
|||
Line 3: | Line 3: | ||
==Solution== | ==Solution== | ||
+ | Notice that over mod <math>2023</math>, we have <math>2022^{2021^{2020^{\dots}}}\equiv(-1)^{2021^{2020^{\dots}}}</math>. Since the power is odd, we conclude that the remainder must be <math>-1\equiv\boxed{2022}</math>. | ||
+ | |||
+ | ~eevee9406 |
Revision as of 20:24, 19 March 2025
Problem
Compute the remainder when is divided by
.
Solution
Notice that over mod , we have
. Since the power is odd, we conclude that the remainder must be
.
~eevee9406