In the set of positive integers including zero, (0,1,2,3,4, ...) this is true about the additive inverse of 7 under addition modulo 9. Pick the correct answer here: 1. It has infinitely many additive inverses. 2. It has no additive inverse. 3. It has exactly two additive inverses which are 2 and 11. 4. It has only one additive inverse which

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A: Let e be the identity element. Hence, it can be written that a*e=a .

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A: second option is correct answer.

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A: I hove used the theorem on congruent

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A: We have to find the moduler multiplicative inverse of a.

Q: If dįd2dzdądzded7ds is 1 4 0 5 7 3 2 3, let n = 100 + dzds and a = dzdg. n 3D Find d e Z, such that…

A: The solution follows from the Generalized Euclidean Algorithm for finding GCD.

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A: Given : A={0,1,2}    To Find : Inverses of A={0,1,2} under a*b=a+b (modulo 3)

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A: The given question is solved below.

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A: Let e be the identity element which exist.  Then, a*e = e*a = a

Q: 1. Use Euler's Theorem to prove a 265 = a (mod 105) for all a E Z.

A: To prove:                   a265≡amod 105 for all a∈ℤ by using Euler's theorem.   Euler's theorem:…

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

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Q: a) Prove that for all integers n > 0, 10" = 1(mod 9). You may refer to theorems from class or the…

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

A: Introduction: Congruence modulo relationship is one of the important relations in number theory. For…

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Q: 1. Use Euler's Theorem to prove a = a (mod 105) for all a E Z.

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Q: |Let A = {n € N| n is a prime divisor of 1840} and let B = {m € N | m is a prime divisor of 1134}…

A: A=n∈ℕ| n is a prime divisor of 1840 Prime divisor of 1840 are 2,2,2,2, 5, 23 So, A=2, 5, 23 ⇒A=3

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

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A: The given statement is False.  Consider, x = 5 and d = 4. Then we see, x2 - 3x = 52 - 3x5…

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