Erdős's conjecture on moments of gaps between reduced residues

Let $q$ be a natural number, let $P=\phi(q)/q$, and let $1=a_1<a_2<\cdots$ be the integers coprime to $q$. Define

$$V_\lambda(q)=\sum_{i=1}^{\phi(q)}(a_{i+1}-a_i)^\lambda.$$

Erdős's conjecture. The gaps between consecutive reduced residues should satisfy

$$V_2(q)\ll \phi(q)P^{-2}=qP^{-1},$$

and, more generally,

$$V_\lambda(q)\ll qP^{1-\lambda}.$$

The source presents this as Erdős's analogue of a conjectural estimate for moments of prime gaps; no resolution is supplied in the given text.