Continue the two sequences of numbers below and find an equation to calculate the n-th value: n 1 2 3 4 5 6 7 Equation an 2 5 10 17 26 37 bn 1 2 8 48 384 3840

Find all x ∈ R that solve this equation: x^4+x^2-x-1=1-x-x^2-x^4

Prove that n^5 − n is divisible by 5 for all positive integers n.

The drawing below shows two squares with side lengths a. One of the squares is rotated by 45◦ and placed in the centre of the second square. Find the surface area of the rotated square not overlapping the non-rotated square (grey area).