# Knot theory and colourability

Going through textbook exercises I have come across this question;

Suppose L is an n-link which is p-colourable $n\in \mathbb{N}$, p a prime.

Under which conditions on n and p can you conclude that L will be trivial. Justify your answer.

Now I understand that if the link was trivial then we can only assign it 1 colour, but under what conditions will it be trivial ?

• Since you are talking about links, there are more colorings than one for the trivial link. – N. Owad Jan 7 '17 at 14:31