It is evident from Fibonacci sequence mod(3) $$ 1,1,2,0,2,2,1,0,1,1,2,0,...$$ that every fourth term of the Fibonacci sequence is a multiple of $3$.

Similarly for mod(5) $$1,1,2,3,0,3,3,1,4,0,4,4,3,2,0,2,2,4,1,0,1,1,2,....$$ suggests that every fifth term in the Fibonacci sequence is a multiple of $5$.

It has been shown that every positive integer n divides the terms of the Fibonacci sequence periodically. The period depends on n .

Question: Is it possible to express the period p as a function of n? For example we have to get p(3)=4 and p(5)=5.