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What is the remainder obtained when $$15^{23}+19^{23}$$ is divided by 17?

Note by Puneet Pinku
1 year, 12 months ago

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$$15^{23}+19^{23} \equiv (-2)^{23}+2^{23} \equiv -1((-2)^3)-1((2^3)) \equiv 0 \pmod{17}$$.

- 1 year, 12 months ago

Thanks, for the beautiful answer. I was totally perplexed as it was not even solved with Euler's, Fermat, or Wilson's theorem. Now, I see the answer comes just from the basic properties of modular arithematic. Thanks a lottttt!

- 1 year, 11 months ago