10th International Mathematical Olympiad 1968 Problems & Solutions

A1.  Find all triangles whose side lengths are consecutive integers, and one of whose angles is twice another. A2.  Find all natural numbers n the product of whose decimal digits is n2 - 10n - 22. A3.  a, b, c are real with a non-zero. x1, x2, ... , xn satisfy the n equations:         axi2 + bxi + c = xi+1, for 1 ≤ i < n         axn2 + bxn + c = x1 Prove that