In GF(2), find the inverse of x^3+1 modulo x^5+x^4+x^3+x+1. Show your complete solution. O a. x^4+x^2+x+1 b. x^3+x^2+x+1 C. X^4+x^3 O d. x^3+x

Q: Suppose that {an} is defined recursively by: an = (an-1)² - 1 and that ao = 2. Find a2 and az.

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Q: Show that MnXn and Rn^2 are isomorphic.

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Q: In GF(2^8), find the multiplicative inverse of (x^7+x) modulo (x^8 + x^6 + x^5 + x + 1). Use table…

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Q: Decrypt the message "PYZTP" which was coded using the key f(a) 19a +1 mod 26. Provide full details…

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Q: ind witnesses to show that n^3 − 5n^2 − 4n is O(n^3).

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Q: Rationalize the denomi 20 5/10 - 7/5

A: 20510-75

Q: for 3^800 how can I find the last digits of it by using mods (such as last digit and 2nd last…

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Q: Which of the following is equivalent to 3x²(-2x)e-x² + e-x²16x O -16xe-x²(x² - 1) O 16xe-x²(x² + 1)…

A: Given query is to simplify the expression.

Q: Write out the first three terms in the expansion of (x + y)^20

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Q: Divide x+2 x²+3x-10 x²-2x-8 x+3

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Q: Find a counter example for the following: For all integers x, if 12 | x^2 then 12 | x.

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Q: Simplify: x*- 4x-5 x* +2x+1 ペ-25 O A. x+1 x-5 В. ** +1 ○c.ピー5 x +1 x²-25 O D. x-1 x-5 OE. x* -1

A: We write x⁴-4x²-5 =x⁴-5x²+x²-5 =x²(x²-5)+(x²-5) =(x²+1)(x²-5) Also x⁴+2x²+1 =(x²+1)²

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Q: How do we know that -1 and -2 will be in the field?

A: Given F is field, So,  0, 1∈F ( since a field F must contain zero element and unity ) A field is…

Q: 3x-11 mang má O a. Inkx+6Xx-17+c O b. In x-1)(x+67+c Ocinkx+1Xx-6+c Od. Inx-6)(x+1)+c

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Q: Letr = (15462 37) and q = (2 4 5 6) be permutations in S7, written in cycle notation. What is the…

A: The given permutations are r=(1 5 4 6 2 3 7) , q=(2 4 5 6). To write: The second line of r in…