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 \(p \, |\, S_k\).

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...

## Comments

Sort by:

TopNewestall values of \(k\) such that \(p-1\) does not divide \(k\). – Brilliant Member · 1 year, 6 months ago

Log in to reply

Some solutions are k=1,2,3,p – Samarth Agarwal · 1 year, 7 months ago

Log in to reply

– Lakshya Sinha · 1 year, 7 months ago

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