Prove, by mathematical induction, that 5ⁿ + 3 is divisible by 4 for all non-negative integers n.

Prove by mathematical induction that, for all non-negative integers n, 11^(2n) + 25^n + 22 is divisible by 24.

The sequence a1, a2, a3, ... is such that a₁ > 5 and an+1 = 4an/5 + 5/an for every positive integer n. Prove by mathe…

Prove by mathematical induction that, for all positive integers n, 10ⁿ + 3 × 4ⁿ⁺² + 5 is divisible by 9.

The square matrix A has λ as an eigenvalue with e as a corresponding eigenvector. Show that e is an eigenvector of A²…

The plane Π₁ has equation r = [[2], [3], [-2]] + s[[1], [0], [-1]] + t[[0], [-1], [-2]]. Find a cartesian equation of…

The curve C has parametric equations x = t², y=t-t³, for 0 ≤ t ≤ 1. Find the surface area generated when C is rotated…