Circle of Liars - The Truth Claim

In a circle, `n` people are seated, each of whom is either a liar or a truth-teller.

The people are looking towards the center of the circle. A liar always lies, and a truth-teller always tells the truth.

Each of the people knows exactly who is a liar and who is a truth-teller.

Each of the people says that the person sitting two places to their left (that is, next to the person sitting next to them), is a truth-teller.

It is known that in the circle there is at least one liar, and at least one truth-teller.

a. Is it possible that `n = 2017`?

b. Is it possible that `n = 5778`?

(Solution format: "word, word" for example "cat, puppy")