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a. Using the Euclidean Algorithm and Extended Euclidean Algorithm, show that gcd(99; 5) = 1 and...

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Advance Math

a. Using the Euclidean Algorithm and Extended EuclideanAlgorithm, show that gcd(99; 5) = 1 and find integers s1 and t1such that 5s1 + 99t1 = 1.
[Hint: You should find that 5(20) + 99(?1) = 1]


b. Solve the congruence 5x 17 (mod 99)


c. Using the Chinese Remainder Theorem, solve the congruence
x 3 (mod 5)
x 42 (mod 99)


d. Using the Chinese Remainder Theorem, solve the congruence
x 3 (mod 5)
x 6 (mod 9)
x 7 (mod 11)

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