1st International Mathematical Olympiad 1959 Problems & Solutions

A1.  Prove that (21n+4)/(14n+3) is irreducible for every natural number n. A2.  For what real values of x is √(x + √(2x-1)) + √(x - √(2x-1)) = A given (a) A = √2, (b) A = 1, (c) A = 2, where only non-negative real numbers are allowed in square roots and the root always denotes the non-negative root? A3.  Let a, b, c be real numbers. Given the equation for cos x: