Hi verybody,

Is there a proof of:

Sum[(i^s - 1), {i, 1, a}] mod( a ) = Sum[(i - 1)^s, {i, 1, a}] mod(

a )

a, s positive integers (could be equal).

If there is, please tell me.

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- Jun 21st 2009, 08:19 AMgdmathSum of powers
Hi verybody,

Is there a proof of:

**Sum[(i^s - 1), {i, 1, a}] mod( a ) = Sum[(i - 1)^s, {i, 1, a}] mod(**

**a )**

a, s positive integers (could be equal).

If there is, please tell me. - Jun 21st 2009, 08:47 AMBruno J.
Are you saying

? - Jun 21st 2009, 09:33 AMgdmath
exactly (a>s)

- Jun 21st 2009, 02:01 PMBruno J.

and

because both sums are taken over complete residue systems . Works also if b.t.w.