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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:

Why do this problem?

For practice in factorising polynomials.

Key question

What is the highest power of 5 we can find using a calculator?

Can we factorise this expression to get factors involving smaller powers of 5, so that all the powers of 5 can be found using a calculator?

Howdo you know if a number is divisible by 3?