Difference between revisions of "2023 SSMO Relay Round 1 Problems/Problem 1"
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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>. | 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>. | ||
− | + | Determine the value of <math>1+\frac{1}{2+\frac{1}{1+\frac{1}{2+\frac{1}{1+\cdots}}}}</math> |
Revision as of 20:30, 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
.
Determine the value of