ted +n; the second will resemble ordinary multiplication and be De denoted Xn DEFINITION 4.7. Given p, q E {0, 1, 2, - . ,n – 1}, define: i) p +n q to be the remainder when p+q is divided by n, and ii) p Xn q to be the remainder when p x q is divided by n. These operations are referred to as addition mod(n) and multiplication mod(n), respectively. ACTIVITY 4.21. Use the above definitions to calculate each of the following in the set Z12. (a) 3+12 6 (b) 8 +12 7 (c) 3 x12 6 (d) 8 x12 7 -...pdf

Q: Q. Now make a multiplication table for modulo 3. ol 1 2 IN 0 1 2

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

Q: 5. Evaluate : 23391 mod 55 (use modular exponentiation)

A: We Know that Modular exponentiation is a type of exponentiation performed over a modulus.

Q: Evaluate: 3135 mod 59. (Note that 3519 = 1000112) %3D

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Q: What is the multiplicative inverse of 4 Mod 11? 06 0 1 09 O 3

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Q: . Determine whether or not x³ + 2x + 1 and x4 + 3x - 2 are congruent mod (x² + 2x + 2) in Q[x].

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Q: ou are told that 159238479574729 = 529

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Q: 2 34 5 6 7 8 9 X (b) 9 3 716 5 2 X 4 8 (c) (abc)(cad) (d) (213)(3421)(153)

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Q: 2. Determine x >0 for each case: 5903 = x (mod 60), 17342 =r (mod 5).

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Q: Compute Re if z₁ = 5√√2 + 2√3i, and z2 = 3√√√2-5√3i 2

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Q: (c) Find integers p and q so that 17p + 45q = 1. Show your working steps. (d) Using the result in…

A: Given that 17p+45q=1 has no solution such that p and q are integers which means gcd of (17, 45) is 1…

Q: QUESTION 12 Show by contraposition that for all integers n, if „2 is odd, then n + 1 is even. For…

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Q: Explain what is meant by the statement “c is the inverse of a (mod 5)”.

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Q: Decryption Stage While everyone can do the encryption using public (n,e), not everyone can decrypt.…

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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.

Q: Compute (3714 - 39) mod 9 without a calculator.

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

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Q: if a-1 is the inverse of a mod m and b-1 is the inverse of b mod m then a-1b-1 is the inverse of ab…

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Q: If 3x + 2 = 0 (mod 7), which of the following values can x assume? О а. -3 O b. 0 О с. 2 O d. -1

A: Given 3x + 2 = 0 (mod 7).

Q: Find the inverse of 13 modulo 47

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Q: Is -3 a multiplicative inverse of 17 mod 26? Show all workings.

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Q: For each of the following pairs, determine whether they are congruent modulo (b) 132 and 10 11.…

A: Given below the detailed solution

Q: If(20.02)Ba) ane mod pocnt of sides oc, CA AA A ABC, them the eguntrom of AB is リ2メ-39-3-0 2 2メナ4=0…

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Q: Use the modular inverses found in the preceding problem to solve the following congruences, if…

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Q: (d) 357 862 193 = (mod 943). (e) 5327 6135 7139 2187 5219 . 1873 = (mod 8157). (Hint. After each…

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

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Q: Consider Z₁1 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Part A. Denote by +11 the operation "addition…

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Q: Let x Є Z. Prove that if x2 - 8x + 11 is divisible by 4, the x6-1 is also divisible by 4.

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Q: QUESTION 5 Consider the linear combination 1 = 13(3) + 19(-2) then, a. The multiplicative inverse of…

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Q: Show that - a is not the inverse of a e N for the addition operation + on 1 N and - is not the…

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Q: (d) For all integers a and b, if ab = 7 (mod 12), then either a = 1 (mod 12) or a = 7 (mod 12).

A: (d) For all integers a and b, if ab=7 mod 12, then either a =1 mod 12 or a =7 mod 12

Q: use the Euclid's algorthim to find the inverse for 76 mod 83

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Q: False In mod 7 arithmetic,

A: Introduction: Modular arithmetic is an integer-based arithmetic method that takes the remainder into…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.