MathDB

Points

A_1, \ldots A_n

with rational coordinates lie on a plane. It turned out that the distance between every pair of points is an integer. Prove that there exist points

B_1, \ldots ,B_n

with integer coordinates such that

A_iA_j=B_iB_j

for every pair

1 \leq i \leq j \leq n

N. Sheshko, D. Zmiaikou

3.4