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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
It is worth emphasising the cyclic nature of this recurrence relation.

What happens with different starting numbers and why?