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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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2 \times 3

2^{34}

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

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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!

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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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

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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!

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