29th British Mathematical Olympiad 1993 Problems

29th British Mathematical Olympiad 1993 Problems1.  The angles in the diagram below are measured in some unknown unit, so that a, b, ... , k, l are all distinct positive integers. Find the smallest possible value of a + b + c and give the corresponding values of a, b, ... , k, l. 2.  p > 3 is prime. m = (4p - 1)/3. Show that 2m-1 = 1 mod m. 3.  P is