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I want to know why the distribution the points in Elliptic curves over a finite field $\mathbb{F}_p$ where $p$ is prime is uniform. That means the number of points in elliptic curve $E$ with $x$-coordinate in the interval $[0,p/3][p/3,2*p/3][2*p/3,p]$ is roughly equal.

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    Look at Sato–Tate conjecture (if $E$ has no CM).2018-11-23

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