I have to prove that the next equality holds:
p−1∑k=0(k(k+a)p)=p−1∑k=0(k(k+1)p)
with a∈Z and a not divisible by p and p prime. I am supposed to use a substitution for this, but I have no idea which one.
Afterwards I have to use this equality, together with this one (which I already proved)
p−1∑k,l=1(klp)=0
to prove that
p−2∑k=1(k(k+1)p)=−1.
Any help would be appreciated!
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