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

Note by Puneet Pinku
2 months, 1 week ago

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\(15^{23}+19^{23} \equiv (-2)^{23}+2^{23} \equiv -1((-2)^3)-1((2^3)) \equiv 0 \pmod{17}\). Svatejas Shivakumar · 2 months, 1 week ago

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@Svatejas Shivakumar 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! Puneet Pinku · 2 months ago

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