--- In

primenumbers@yahoogroups.com,

"John" <mistermac39@...> wrote:

> > No integral point Q on E(-27*k) results

> > from a rational point P on E(k)

>

> I suspect this means there is no mapping, and one to one

> or any other correspondences

There are fancy names like injection and surjection

that I tend to get the wrong way round. I think the

right way round is to say that the map is injective,

but not surjective.

My heathen way of putting it is to say that every Q is mapped to

by at most one P. But there are lots of Q's that are mapped to

by no P's. And in the present case those Q's not given by P's

include all the integral points that form Mike's data.

At first I found this rather annoying. But then I realized that

it provides a wonderful blind check, whose validity is widely

believed, but not yet proven at the million-dollar mark.

David