hhhhhh, yes I read it and I gave him an answer I told that I already find that: $(n^2)^{1+2k} \equiv -1 \mod{p}$
that's was the question of the exercise then the next question is to prove $(n,p)=1$ then the next question is $(n^2)^{1+2k} \equiv 1 \mod{p}$ not -1 this time to find a contracdition in the end.