Question 52
There are $n$ points $A_1, \dots, A_n$ on the plane with rational coordinates, all pairwise distances between them being integer. Prove that there exist points $B_1, \dots, B_n$ on the plane with integer coordinates such that $|B_iB_j| = |A_iA_j|$ for all $1 \le i \lt j \le n$.