Friday, 28 July 2017

number theory - How to prove equality of sum of Legendre symbols

I have to prove that the next equality holds:
p1k=0(k(k+a)p)=p1k=0(k(k+1)p)
with aZ 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)
p1k,l=1(klp)=0



to prove that
p2k=1(k(k+1)p)=1.



Any help would be appreciated!

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