Let be a prime number. Stating any results that you use, deduce that xº-1 = (x – 1)(x – 2) · . · (x – (p – 1)) (mod p), •. and so for p > 3, (p – 1)! = -1 (mod p).

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Q: Let_Z1 = 3 + i and Z2 = 5 + 2 i . Find 2 Z1 /( Z1 - Z2) - (14/5)-2 i O (14/5) + 2i O - (14 / 5) + (…

A: Topic = Complex number

Q: Limzoo (√x² + 4x +1 − x) O a. 2 O b. none of these O c. -1 Od. -2 O e. 1

A: The objective of the question is evaluate the limit and choose the correct option.

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Q: 22. Why does the risk of a Type Il error increase as we decrease a, the Type I error?

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Q: Find integers x and y so that gcd(3953, 1829)=3953x+1829y. x=2,y=5 x=-12,y=-13 x=-6, y=13 x=6,y=-13…

A: Solution:we have to find integers and so that first we find gcd of (3953,1829)here we see that…

Q: Let G = Z and H=3Z. Decide whether or not the following cosets of H a written in additive notation).…

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Q: Find the smallest positive integer x such that 11x + 567y = 5 for some integer y. Enter x below.

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Q: If find |A| = A = -1-20 [4+4i-1-21] 3-i

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Q: Let A = 2 0 and 1 -1 2 3. find A+(28)"

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A: Answer is in next step

Q: For any positive integer n, prove that 6|n(7n² + 5).

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Q: For -3-3: (a) Find the modulus and argument of z. (b) Express + in the form of a+ib where a,beR.

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Q: If Xo and X, are two numbers with Xo F(X1) d. F(XO)<F(X1)

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Q: Evaluate G r. d.x. (x2+1)(x+1) 0.

A: The following integrals are useful, while evaluating the integral that is provided. ∫dxx =ln x +C…

Q: Prove the following for Integers x and y, (17 | 10x + 8y) = (17 | 3x + 16y)

A: 17 | 10x + 8y where x and y are integers =&gt; 10x + 8y = 17m for some integer m