For a given prime \(p > 2\) and positive integer \(k\) let \[ S_k = 1^k + 2^k + \ldots + (p - 1)^k\]

Find those values of \(k\) for which \(p \, |\, S_k\).

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

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

Sort by:

TopNewestall values of \(k\) such that \(p-1\) does not divide \(k\).

Log in to reply

Some solutions are k=1,2,3,p

Log in to reply

k should not be the multiple of \( \phi (p) \) will always satisfy.

Log in to reply