More fun in 2016, Part 6

We have the three trivial solutions $(0,0$ and $(\pm 2016,0)$ , but are there more?

In Part 4 of this fun-filled Series we found the arithmetic progression $47^2, 65^2, 79^2$ with common difference 2016. Thus $(47*65*79)^2=47^265^279^2=(65^2-2016)65^2(65^2+2016)=65^3-2016^2*65$ , so that $(65^2,47*65*79)$ $=(4225,241345)$ is a fourth integer point on our curve. We conclude that there are $\boxed{> 3}$ such points.

More generally, if $a^2<b^2<c^2$ is an arithmetic progression with common difference $n$ , for rational $a,b,c$ , then $(b^2,abc)$ is a nontrivial rational point on the elliptic curve $y^2=x^3-n^2x$ .