We can extend the definition of the gcd of two numbers to the gcd of three or more

Chapter 36, Problem 36.10

(choose chapter or problem)

We can extend the definition of the gcd of two numbers to the gcd of three or more numbers. a. Give a careful definition of gcd.a; b; c/ where a; b; c are integers. b. Prove or disprove: For integers a; b; c, we have gcd.a; b; c/ D 1 if and only if a; b; c are pairwise relatively prime. c. Prove or disprove: For integers a; b; c, we have gcd.a; b; c/ D gcd a; gcd.b; c/ : d. Prove that gcd.a; b; c/ D d is the smallest positive integer of the form ax Cby Ccz where x; y; z 2 Z. e. Find integers x; y; z such that 6x C 10y C 15z D 1. f. Is there a solution to part (e) in which one of x, y, or z is zero? Prove your answer.