Question 6 (14 marks) (a) Suppose that a and b are integers such that a = 11 (mod 23), and b= 5 (mod 23). Find the integ

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Question 6 14 Marks A Suppose That A And B Are Integers Such That A 11 Mod 23 And B 5 Mod 23 Find The Integ 1 (17.7 KiB) Viewed 32 times

Question 6 (14 marks) (a) Suppose that a and b are integers such that a = 11 (mod 23), and b= 5 (mod 23). Find the integer z with 0 S=522 such that z = 2a +36 (mod 23). [3 marks] (6) 1) Use the Euclidean Algorithm to find ged(7239, 3519). [3 inarks] (í) Hence, write the gcd as a linear combination of 7239 and 3519. [3 marks] © Find the inverse of 8 modulo 23 by first finding Bezout coefficients of 8 and 21. [3 marks] (d) Hence or otherwise, solve the following for x when &r = 10 mod 23. [2 marks]