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Solving for the last two digits of a large number $3^ {1000}$? I found this question asking to find the last two digits of $3^{1000}$ in my professors old notes and review guides What material must I know to solve problems like this with remainders I know W
Infected Dinner Brainteaser - Mathematics Stack Exchange I came across this brainteaser online that I found quite confusing: There are $1000$ people having dinner at a grand hall One of them is known to be sick, while the other $999$ are healthy Each m
elementary number theory - How to find the last digit of $3^ {1000 . . . The last digit of $3^5$ is $3$ The last digit of $3^6$ is $9$ Notice a pattern? Why does this pattern exist? What is going on when I multiply by three? Based on this we could guess that it has a period of $4$ so that $3^ {4n}\equiv 1$ Use this to find the last digit of $3^ {1000}$ (Do you know modular arithmetic? If so it is a lot easier)