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

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TopNewestall values of \(k\) such that \(p-1\) does not divide \(k\). – Svatejas Shivakumar · 1 year, 2 months ago

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

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– Lakshya Sinha · 1 year, 2 months ago

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