代做MATH 3175 GROUP THEORY QUIZ 1帮做R编程

QUIZ 1 (20 MIN, OPEN BOOK)

MATH 3175 GROUP THEORY

(Each problem is worth 10 points.)

(1) (a) Compute the greatest common divisor (321, 231) of 321 and 231 using the Euclidean algorithm. Show your steps.

(b) Use a systematic approach (i.e., not just trial and error) to find integers m and n such that (321, 231) = 321m + 231n.

(2) Prove that if a and b are integers with a | b, then a 2 | b 2 .

(3) Suppose that p and q are distinct primes. Show that (p, q) = 1.