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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.

Production Equation

Age 16 to 18
Challenge Level
The general method of solving problems where there is a formula for the transition from one phase to the next is to solve either a difference equation (such as this), or a differential equation, according to whether the model is discrete or continuous.