Question: (ir) 2. (i) Use Euclid's algorithm to show that gcd{589, 779) = 19. (*)[ii) Write 19 as an integral linear combination of 589 and 779.

(ir) 2. (i) Use Euclid's algorithm to show that gcd{589, 779) = 19. (*)[ii) Write 19 as an integral linear combination of 589 and 779. (*)[iii) Find all solutions (my) 6 32 to the homogeneous equation 589: + 7793; = 0. (*)[iv) Find all solutions (my) E Z2 to the equation 589: + 7793; = 19. (*)[v) Find all solutions (:12, y} E Z2 to the equation 5891: + 779g = 19[}. (*)[vi) Find all solutions (Ly) E Z2 to the equation 5393 + 779;; = 119

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