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.

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:

Factorise $5^{36}-1$ into as many factors as you can, until you can
calculate the values and see which ones are even and which are
multiples of $3$.