QuestionQuestion

1) Use the Euclidean Algorithm to solve the equation 135x+ 112y= 6649 for all integer solutions.

2) Find all solutions of 3x≡7(mod12)

3) Find the inverses of 10 and 12 modulo 14.

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Problem 1
135x+112y=6649
First, we find GCD(135,112) using Euclid’s algorithm.
135=1*112 + 23 => 23= 135-112
112= 4*23 + 20 => 20 =112- 4*23...

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