Find all positive integers \(n \geqslant 2\) for which there exist \(n\) real numbers \(a_1<\cdots<a_n\) and a real number \(r>0\) such that the \(\tfrac{1}{2}n(n-1)\) differences \(a_j-a_i\) for \(1 \leqslant i<j \leqslant n\) are equal, in some order, to the numbers \(r^1,r^2,\ldots,r^{\frac{1}{2}n(n-1)}\).