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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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Absurdity Again

What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?

Pair Squares

Age 16 to 18 Challenge Level:

The numbers $2$, $34$ and $47$ are such that the sum of any pair of these numbers is a perfect square. Find a method for choosing three square numbers and from them finding a corresponding set of three integers with this property and give some examples.

The integers $-208$, $224$, $352$ and $737$ also have the property that the sum of any pair of these numbers is a perfect square. Find other sets of four integers with this property.