How would one show that the number of points on the elliptic curve y^2=x^3+B, defined over F_p is p+1, when p is congruent to 2 mod 3?
Thank you
You mean over projective space, right? Anyway, as , the map is an automorphism of , and thus is a bijection between the set of points of the elliptic curve in . Now add the point at infinity in projective space and we're done.