In the set {0,1,2,3,4,5}, this is the additive inverse of 4 under addition modulo 6. What is the correct answer?

Q: The multiplicative inverse of 19 (mod 141) * O is 51(mod 141) None of these O is 19(mod 141) is…

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Q: Find the additive inverse and the multiplicative inverse, if it exists, of the given number.  4 in…

A: We will solve this using definition of additive and multiplicative inverses

Q: The prime number 8191 is a None Inverse of 7 modulo 11 Carmichael umber Mersenne prime mmber

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Q: The modular representation of the integer 23 with respect to the modulo 2, 3, 5 is (1,2,3) (3,2,1)…

A: the modular representation of the integer 23 with respect to the modulo 2,3,5 is it is known that…

Q: If a= b (mod n) and gcd (a, n) = d, then gcd (b, n) = d :Select one True False

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Q: Find the inverse of 42 (mod 8) or state why it cannot exist. Find the inverse of 17 (mod 5) or state…

A: Given: a) Find the inverse of 42(mod 8) or state why it cannot exist. b) Find the inverse of 17(mod…

Q: The easiest way to evaluate 2 8 5 -4 3 5 7 0 is to expand about the elements in -6

A: A square matrix is a matrix whose number of rows and columns is the same. Determinant can be…

Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?.

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Q: Compute the addition modulo operation 3+2 2 0. 1 3 O O

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Q: Consider 3 · 1, 3 · 2, 3 · 3, . . . , 3 · 12 all mod 13, or in other words, the multiples of 3 in…

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Q: a) Show that ac = bc mod cd if and only if a = b mod d

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Q: The set {0,5,6} is closed under Mod(10)

A: To check if { 0 5, 6} is closed under mod(10)

Q: What is the multiplicative inverse of 21 in mod 23?

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Q: Number theory

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Q: In mod n arithmetic why does x have a multiplicative inverse if and only if x is relatively prime to…

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Q: Al. b. Find the inverse of 17 modulo 23, if exists. If not, give reasons.

A: The objective is find the inverse of 17 modulo 23 if exists or else give the reason why it does not…

Q: Let a, n be positive integers. Knowing that 15a - 13n = 1, we deduce that the multiplicative inverse…

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Q: If gcd(7, a) = 1, prove that either a +1 or a – 1 is divisible by 7. 20

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Q: Make a table multiplication mod 6

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Q: 1. Show that an integer n is divisible by 2 if and only if its last digit is even. (Hint: For each i…

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Q: In the set of positive integers including zero, (0,1,2,3,4, ...) this is true about the additive…

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Q: In mod n arithmetic why does x have a multiplicative inverse if and only if x is relatively prime to…

A: Note that, two integers are relatively prime if and only if their greatest common divisor is 1. The…

Q: 3. Find an inverse, if exists, of 12 mod 15.

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Q: The Modular class of [2] under modulo 8 is O [2] = {..., -8,-4,2,4,8,...} [2]={…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: The affine cipher E is given by E(x) ≡ 15x − 7 (mod 26). The conversion table for letters and…

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Q: If (a, 42) =1, then a^6-2=?mod 168 1 -1 None of these

A: Just apply the Fermat's Theorem.

Q: True or False For arbitrary integers a and b, a ≡ b(mod n) if and only if a and b do not have the…

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Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?

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Q: Is multiplication modulo 6 a binary operation on Z6^*? why or why not?

A: Take two elements in the set.Check whether multiplication modulo 6 of two elements is again in the…

Q: Prove (1.2), (1.3), and (1.4).  

A: (a) Let x∈A∪B So, ⇔x∈A or x∈B⇔x∈B or x∈A⇔x∈B∪A So, A∪B=B∪A

Q: The multiplicative inverse of 19 (mod 141) * is 52(mod 141) is 19(mod 141) is 51(mod 141) None of…

A: We have, 141 = 19×7 + 8 So, 19 = 8×2 + 3 So, 8 = 3×2 + 2 So, 3 = 2×1 + 1 So, 2 = 1×2 + 0 So,…

Q: Determine the remainder of 102020 modulo 2020 and the remainder of 102020 modulo 2021.

A: solution 104≡1920(mod2020)…

Q: If 3x = 6 mod 9, when -2 <x< 8. Then O x=(-1, 3, 5} x=(-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

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Q: Number theory

A: According to the given information, it is required to find multiplicative inverse of 4 modulo…

Q: If AB = -BA, then A and B are said to be anticommutative. Are A = 1 and B = anticommutative?

A: Since, we have been given that A=0-110 and B=100-1,then our aim is to show that whether A and B are…

Q: Construct the addition and multiplication table for Z4 (Note that, both operations are mod4)

A: We have to solve given problem:

Q: The multiplicative inverse of 103 (mod 120) * O is 7(mod 120) O None of these is 50(mod 120) is…

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Q: Give an example to show that a ^2 ≡ b^2 (mod m) need not imply that a≡ b (mod m)

A: Here I listed given example of above statement.

Q: If 3x = 6 mod 9, when -2 < x< 8. Then O x={-1, 3, 5} x-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

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Q: Which of the following sets is dlosed under the given operation? O {1, 4, 5, 7} multiplication mod 9…

A: Group. Solving ques 1 According to guidelines.

Q: Show that af +...+ a, = a1 + ...+ ap(mod p).

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Q: Find a multiplicative inverse of  21 modulo 46

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Q: Find the additive and multiplicative inverse of the following 4 in modulo 9 arithmetic 7 in modulo…

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Q: 5. If a-l is the inverse of a modulo m and b-1 the inverse of b modulo m, show that a--1 is the…

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Q: According

A: We know that,  If a, p are integers and p is any prime such that gcd(a,p)=1 then ap-1=1 mod p.

Q: Which of the following sets is closed under the given operation? O {1, 4, 13} multiplication mod 15…

A: {0,4,8,16} addition mod 16 And 2/x

Q: find the additive inverse and the multiplicative inverse,if it exist, of 5 in modulo 9 arithmetic.

A: We have to find the additive inverse and the multiplicative inverse, if it exist, of 5 modulo 9.…

Q: 36. List all the elements of G* . G = Z/36Z

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Q: Number theory

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