MAS 4214/001 Elementary Number Theory, Fall 2013CRN: 80553Answers, Set 3Question 1.(2 pts)(Exercise 11.5 with bigger integers.) Compute gcd(6982799,5605027,7224977).

Question 2.(1 pt)(Similar to Exercise 11.6)Suppose thatℓ≥2. Letai∈Zfori= 1,2,...,ℓ. Prove that if gcd(a1,a2) = 1 then gcd(a1,a2,...,aℓ) = 1but the converse is false.

Question 3. (2 pts) Leta,b,c,d∈Z. Prove that gcd(abc+abd+acd+bcd,abcd) = 1 if and only ifa,b,c,dare pairwise relatively prime.