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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.

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Fibonacci Factors

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

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Code to Zero

Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.

Powerful Factors

Age 16 to 18 Challenge Level:

Use the following identities:

$x^2-y^2 \equiv (x-y)(x+y)$

and

$x^3+y^3 \equiv (x+y)(x^2-xy+y^2)$

to find the highest power of $2$ and the highest power of $3$ which divide $5^{36}-1$.