Logic: Knights and Liars Question from the Russian Olympiad. (Translated with Google Translate, with a translation fix.):

In a circle there are $181$ people, each of whom is either a knight or a liar (liars always lie, and knights always tell the truth). Each of those standing said: “Two places away from me there is at least one liar.” 
  Find the smallest possible number of liars among these $181$ people.

My solution:
I first estimated that there were $5$ people then the minimum number of liars is $2$. because $1$ said $3$ liars $2$ said $4$ liars $3$ said $5$ liars and $4$ said $1$ liars and $5$ said $2$ liars. then if $1$ liar then $4$ and $3$ knights. Whence it follows that $4$ is also a liar and $2$ knight. Well, then the minimum number of liars in our case is $90$.

Question:is it correct answer?

EDIT: I’ll try to explain it. Let's say if there are people in a circle with numbers $1,2,3,4,5,6$ ..., $181$ then this means that #$1$ says that either #$3$ or #$180$ is a liar, #$2$ says that either #$4$ or #$181$ is a liar and so forth.
 A: If I understand correctly, everyone in the circle says 2 persons away (in any direction) there is a liar.
The minimal pattern that matches is $KxLyK$ - the $L$ lies because there isn't one, and the $K$'s both tell the truth.
We can interleave two of those patterns and repeat pattern $KKLLKK$ 30 times.
Then you have to close the circle with a $L$. On both sides, the second item is a $K$, which repeats the pattern.
The solution therefor: $61$
A: Your solution for five does not work.  When you assume $1$ is a liar you find $4$ and $3$ tell the truth.  You did not pursue that to say $3$ says $5$ is a liar and must tell the truth, so $5$ is a liar.  Then $5$ says $2$ is a liar, so $2$ tells the truth.  $2$ says $4$ is a liar, which is a contradiction.  The same thing will happen if you assume $1$ tells the truth.  There is no consistent solution.  
It is similar for $181$ or number equivalent to $1 \bmod 4$ in the circle.  If we assume $1$ tells the truth, every fourth person tells the truth up to $181$.  Then $2$ is a liar and so is every fourth person up to $178$.  $180$ tells the truth, saying $1$ is a liar and we have the same contradiction. 
