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For this task, you will be doing some modular arithmetic. You may use a calculator or a computer program to simplify the computations. But you need to justify how it is done.
a. Suppose that a and b are integers such that a ≡ 34 (mod 83) and b ≡ 21 (mod 83). Find an integer c such that 0 ≤ c < 83 such that 47c ≡ (53a -2 + b 5 ) (mod 83)
b. Determine the greatest common divisor of 12852 and 30576.
c. Solve the congruence equation 33x + 47 = 21 in F59.
d. Find an x such that 0 ≤ x < 126 and x ≡ 2 2022 (mod 127).
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