Use the Euclidean algorithm to find the GCD of the following pairs of integers. Also find s and t such that as+bt=gcd(a,b). (a) a=2938 and b=183 (b) a=93182 and b=246 Show all calculations. Does a inverse mod b exist? If yes, what is it.

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A: Answer

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A:

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A: Dear learner, hope you are doing well , I will try my best to answer this question. Thank You!!

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A: Proved the induction (wR)R=w where w is from Σ* are as follows:

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 prove s using natural deduction
.

A: modus ponens (p->q) ^ p - > q Resolution (pVq ) ^(~p Vr) -> (qVr) p->q = ~p V q

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Q: You

A: (a) Brute force: 2^x≡6  (mod 101) 2^x≡6  (mod 569) 2^x≡6  (mod 3) 2^x≡6  (mod 19) 2^x≡6 (mod 31)

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A: The following is the solution

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A: Hence proved. Show explanation below.

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A:

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Fast Fourier Transform Concepts

The algorithm used to convert a sequence to its Discrete Fourier transform (DFT) is known as the Fast Fourier transform. It can be used for both DFT and IDFT (Inverse DFT) transformation.