Posted by **Shrek** on Thursday, April 15, 2010 at 3:57am.

A ¡§lattice point¡¨ has integer coordinates. Then, A = (m, n) is a lattice point if both

m and n are integers. Let¡¦s call a point P = (x, y) ¡§generic¡¦¡¦ if all the distances from P

to lattice points are different.

With some algebraic work, I checked that the point S = ( , ) is generic.

However, the point T = (0, £k) is not generic because it is equally distant from the lattice

points (1, 0) and (-1, 0).

„½ Is there some generic point with rational coordinates?

That is, if Q = (r, s) for rational numbers r and s, must there exist two lattice points

equidistant from Q ?

As a first step, show that R = ( , ) is not generic. (Find lattice points A, B equidistant from R.)

Can you use those ideas to answer the general question?

- Algebra -
**Anonymous**, Friday, May 3, 2013 at 7:21am
But how ???

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