IMC 2006 Problem 10

Let $v_{0}$ be the zero ector and let $v_{1},...,v_{n+1}\in\mathbb{R}^{n}$ such that the Euclidian norm $|v_{i}-v_{j}|$ is rational for all $0\le i,j\le n+1$ . Prove that $v_{1},...,v_{n+1}$ are linearly dependent over the rationals.