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Golden Powers

You add 1 to the golden ratio to get its square. How do you find higher powers?

2^n -n Numbers

Yatir from Israel wrote this article on numbers that can be written as $ 2^n-n $ where n is a positive integer.

Poly Fibs

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.

And So on - and on -and On

Age 16 to 18
Challenge Level

The solution needs you to be systematic.

Start with $ f_{0} $, then work out $ f_{1}$, then work out $ f_{2}$

\begin{eqnarray}f_{0}(2000)&=& \frac{1}{1-2000}\\ &=& \frac{1}{-1999}\end{eqnarray}