26th All Russian Mathematical Olympiad Problems 2000

1.  The equations x2 + ax + 1 = 0 and x2 + bx + c = 0 have a common real root, and the equations x2 + x + a = 0 and x2 + cx + b = 0 have a common real root. Find a + b + c. 2.  A chooses a positive integer X ≤ 100. B has to find it. B is allowed to ask 7 questions of the form "What is the greatest common divisor of X + m and n?" for positive integers m,