The gears D and G are rigidly attached to shafts that are held by frictionless bearings. If rD = 90 mm and rG = 30 mm, determine (a) the couple M0 that must be applied for equilibrium, (b) the reactions at A and B.

Definition 1.1. Given two integers a and d with d non-zero, we say that d divides a (written d | a) if there is an integer c with a = cd. If no such integer exists, so d does not divide a, we write d - a. If d divides a, we say that d is a divisor of a. Proposition 1.2.1: Assume that a, b, and c are integers. If a | b and b | c, then a | c. Proposition 1.3. Assume that a, b, d, x, and y are integers. If d | a and d | b, then d | ax + by. Corollary 1.4. Assume that a, b, and d are integers. If d | a and d | b, then d | a + b and d | a − b. Proposition 1.4. Let a, b, c ∈ Z be integers. a) If a | b and b | c, then a | c. b) If a | b and b | a, then a = ±b. c) If a | b and a | c, then a | (b + c) and a | (b − c). Prime: A prime number is an integer p ≥ 2 whose only divisors are