Expanding and factorising quadratics

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.

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

Can you prove our inequality holds for all values of x and y between 0 and 1?

Use the fact that: x²-y² = (x-y)(x+y) and x³+y³ = (x+y) (x²-xy+y²) to find the highest power of 2 and the highest power of 3 which divide 5^{36}-1.

If you plot these graphs they may look the same, but are they?

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.

This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.