MathDB

Prove that there are different points

A_0 \,\, ,A_1 \,\, , \cdots A_{2550}

on the

XY

plane corresponding to the following properties simultaneously. (i) Any three points are not on the same line. (ii) If

d(A_i,A_j)

represents the distance between

A_i\,\, , A_j

then

\sum_{0 \leq i < j \leq 2550}\{d(A_i,A_j)\} < 10^{-2008}

Note :

\{x \}

represents the decimal part of x e.g.

\{ 3.16\} = 0.16

.
(passer-by)

Problem Statement