Σn∈Fp× Σk∈Fp exp(2πik^2 n/p)
= Σk∈Fp Σn∈Fp× exp(2πik^2 n/p)
= Σn∈Fp× exp(0)
+ Σk∈Fp× Σn∈Fp× exp(2πik^2 n/p)
= (p - 1) + Σk∈Fp× (-1)
= (p - 1) - (p - 1)
= 0