Which of the following elements in Z8000000 is not of order 8? 7 000 000, 2 000 000, 3 000 000, 5 000 000?

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: Determine if g 15 is a primitive element for Z3 if the following is the output for powers of 15 from…

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Q: The generators of Z12 are: O {1,5,7,8,11} O {1,5,7,11} O {1,3,7,11} O {1,3,5,7,11}

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Q: Compute the following.   8C3=

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Q: Label eachof the following statement/s as either true or false.   Every permutation can be expressed…

A: Every permutation can be expressed as a product of disjoint cycles.

Q: D. Let a = (1 2 34 5 145 6 1 2 34 5 2 4 13 6 (1 2 3 4 5 6 52 4316 Compute the following: 1. BY (1 2…

A: Matrix multiplication Rules : The product of two matrices A and B is defined if the number of…

Q: The generators of Z12 are: O {1,3,7,11} O {1,5,7,11} O {1,3,5,7,11} O {1,5,7,8,11} O O O O

A: Generators of Zn are 'a' such that: gcd (a ,n)= 1.

Q: Consider the permutation (1 2 3 4 5 6 \3 4 5 6 1 2 7)* 1. Express as a product of disjoint cycles.…

A: Given Permutation: 12345673456127

Q: Show that A8 contains an element of order 15.

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Q: Compute f2,f3, and f-1 for each of the following permutations.   f= (l,3,7,4)(2,5,9,8,6)

A: f= (l,3,7,4)(2,5,9,8,6)

Q: Compute (12.3 - x) for the following set of n = 5 values. X1 = 0, x2 = 2.9, x3 = 5.5, x4 = 0.4, x5 =…

A: Use the given information to obtain the objective of the problem.

Q: Prove that ?? is generated by the following n-1 transpositions: (1 2), (2 3), (3 4),. . . , (n-1 n)

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Q: 4. Calculate the order of the element 4 in group (Z*18, x mod 18) 5. Calculate the order of element…

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Q: Use Euclid's Algorithm to show that there are integers s and t such that 21s + 97t 1. Showing all…

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Q: Let o be a fixed odd permutation in Sn. Show that every odd permutation in S, can be written as a…

A: The main objective is to prove that every odd permutation can be expressed as σα for some α even…

Q: Prove that (n – 1) +n° + (n + 1)° is divisible by 9 for n E {1,2,3, . }

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Q: Prove by induction that (2n+1)3 is an odd number for all positiveintegers n

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Q: 12. Suppose that k is a divisor of n. Prove that Z,/(k)~ Zp.

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Q: The integers mod 5 (i.e., Z5) form a Boolean algebra, where - addition and multiplication are the…

A: The given question is solved below.

Q: 4 Which of the following is the correct expansion of (3x - 3y)2? 9 x2 - 18 xy + 9 y2 9 x2 - 9 y2 9…

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Q: 8. The Laurent's expansion of (2² – 1) (2² + 4 for |z|<1 is 5z2 2125 1). 4 64 16 2) + 21 4 4 4 3) -…

A: None of the option 1,2,3 and 4 is correct. Please check it.

Q: Let f= (157324) and g = (1 6 7) (2 4) be permutations in S7, written in cycle notation. What is the…

A: The given problem is related with abstract algebra. Given that f = 1 5 7 3 2 4 and g = 1 6 72 4 are…

Q: Show that 1+3/ -5 is irreducible which is not prime in ZlV-5]

A: We know that ,  ℤ-5 = a + b-5 / a , b ∈ ℤ We need to show that , 1 + 3-5  is irreducible but not…

Q: Find the number of inversions in the permutation 52134 of Sz = {1,2, 3, 4, 5}. 6 O 5

A: Number of inversions

Q: X2/ Suppose sr=20142} and c-{ {o8} Enumcrate the cLass of all 6-tields Containing and give cce)

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Q: Consider the following permutations in S7. ) 1234 567 1234567 3254617 2157463 (a) Write the…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Compute |A| for the following:

A: Given, we have to find the determinant of A

Q: Consider the following theorem. Theorem 9.5.1: The number of subsets of size r that can be chosen…

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Q: Which of the following is the given permutation expressed as a product of disjoint cycles? * a =…

A: We have to solve through permutations group

Q: Let r(n) be the number of n-permutations whose square is the identity permutation. Prove that if n >…

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Q: QUESTION 13 List all the elements of order 12 in Z600.

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Q: 4. If G = (Z8,) then G has an element of order 5. *True *False

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Q: Consider the following permutations in S9 1 2 3 O = 4 5 6 7 1 2 3 4 5 6 7 8 9 89 and t = 3 5 1 4 69…

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Q: Let o be a fixed odd permutation in Sn. Show that every odd permutation in Sn can be written as a…

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Q: Suppose that " is in lowest terms and that m< n. Then has a simple-periodic dec- imal representation…

A: Introduction: The ratio of given two numbers could be represented as a factor less than one always…

Q: Find [7]^-1 in Z55 under multiplication.

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Q: Suppose that n > 2 is an even integer and a is an (n – 1) -cycle in S,. Show that a does not commute…

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Q: List all generators of (Z10, +10)

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Q: 2. Let m e N, then show that (a) For integers x, y, x = y(mod m) if and only if the remainder when x…

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Q: Find an element in A12 of order 30.

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Q: Suppose n > 3 is an integer. Prove that in Sn every even permutation is a product of cycles of…

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Q: compute the following in Z12: [9]+[11], [5]-[8], and [7][9].

A: Consider the provided question, We have to find the following in z12:9+11, 5-8, and 79 Find,…

Q: Obtain the generating function for the number of k-part compositions of n in which the ith part does…

A: Solution :-

Q: Construct the multiplication table for Zs. Using this table, or otherwise, determine the following x…

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Q: Find the integer a, if the modular representation of a is (2, 1, 5) with respect to the modulo 3,…

A: We have to find the integer a if the modular representation of a is 2,1,5 with respect to modulo 3,…

Q: Find the term of free x in the 10 2 expansion of (x² + 3)¹0.

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