A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.

For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?

A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?