This is the question I am trying to solve, but while researching about circulant graph I came across Paley's graph of order 13.
There was also a proof I came across, which I could not gather much from, This is the link of the proof. In this they prove that it is true, for odd number of vertices in lemma 2. I am very confused now, am I missing something, is there any other interpretation for this question, my interpretation is that if there is a cycle in the circulant graph, it must be of even length.
Any insights would be helpful.