Didn't understand the solution

egal said:
View attachment 29579
I understand k is odd. But what does d represent?
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It would be really nice if the author had defined it, wouldn't it? This is a little too terse for a proof.

But I think it's clear that d is an integer that varies from 1 to half the number of terms in the given sum. And given that, we can see that they are pairing up terms in the given sum starting from the beginning and from the end, namely 1^k + (p-1)^k, then 2^k and (p-2)^k, and so on. Can you see that?
 
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