I need a solution with an explanation for the following. Thanks!
Let $E/F_q$ be an elliptic curve and let $P ∈ E(F_q)$ be a point
a. if $n=ord(P)>1/2(q^{0.5}+1)^2$ prove that $E(F_q)$ is cyclic of order n
b. if $n=ord(P)>1/m(q^{0.5}+1)^2$ for $m>1$, what can be said about $|E(F_q)|$?