(a) 142021 = r mod 11 (b) 6150 Er mod 72

Q: Which of the following values are needed to compute 406 (mod 37) using fast exponentiation? Mark Y/N…

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Q: Q2: Solve the following (if possible): 1. = 5x + 11 mod 37 3

A: Since you have asked multiple questions, we will solve the first question for you. If you need any…

Q: 9. Show that there are infinitely many primes of the form 16k + 1. More generally, show that for any…

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Q: 43 1040 Determine the length of the pre-period and the length of the period for the decimal…

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Q: The remainder when a is divided by 7 is 2 and the remainder when b is divided by 7 is 5. (So a mod 7…

A: Given that remainder when "a" is divided by 7 is 2

Q: Find the residue for the following case. 86 (mod 7) The residue of 86 (mod 7) is (Round to the…

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Q: 7. Calculate each of the following. [from #22, 4.5] b) 971321 (mod 765) a) 2557341 (mod 5681)

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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: 3. Show that ifn = 2 (mod 4), then 9" + 8" is divisible by 5.

A: Here we will prove the given statement.

Q: (4) Find the values of r in the following equations (such that 0 ≤r <n where n is the integer to the…

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Q: 3) The number 2 is a primitive root modulo 19. Compute the powers 2' for I = 1,2, ..., 18, 19 to…

A: Given: Let us consider Modulo 19, the number 2 is a primitive root. To get the table for the…

Q: # 14 please ASAP

A: We need to evaluate 77 (mod 4).By the Fermat’s Little Theorem,

Q: Find x such that 1577 =x (mod11), 0sx<11. You must show all the detailed steps

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Q: Which of the following is TRUE? -52%3D0( mod 13) OA. -1=-13( mod 13) OB. 446=-278( mod 7) OC. 1=0 (…

A: Only (A) is true.  The detailed solution is as follows below:

Q: Exercise 4.6. Compute the following quantities: (A) 123 DIV 10 (B) 123 MOD 10 (C) 2178 DIV 9 (D)…

A: using the concept of division algorithm and modulo...

Q: Question 3 Solve for x: 32+104 x(mod5) 04 O 2 MAR 21 MacBook Air

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Q: e.g. Student ID=61190003 average=(6+1+1+9+0+0+0+3/8) x 0.01 = 20/8 = 2.5 then round the number to an…

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Q: 4. Let the function g be given by Oniseven 9(n) n =1 (mod 4). n =3 (mod 4) 1 %3D 1

A: This is a question from Number Theory.

Q: Need Answer ASAP Using Fermat's Little Theorem to Calculate Each (Show Your Work) 1. 99 ^ 101 mod…

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Q: Question 2 Make sure that all your answers are explained carefully. (a) Find the remainder of 117…

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Q: (d) Find an integer x, 0 < < 18, that satisfies the following congruence: 9x + 13 = 10 (mod 19).…

A: (d) Given is a congruence 9x+13≡10(mod 19)   To Find: An integer x such that 0≤x≤18 that satisfies…

Q: (a) Prove the following: i. 11 + (6 x 4") - 22n = 6 mod 7, 1 is divisible by 131, ii. 8260 iii.…

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Q: Question 9 Convert the following hexadecimal number to octal O(110011010101)8 (3285)8 (6325)8…

A: The first part of the question asks to convert a hexadecimal number to an octal number. The…

Q: 3. Find all solutions to x² + 5 = 0 (mod 245).

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Q: 11. What do you obtain when you raise 27 to the 8/3 power ? * 1/3 of (27 to the 8th power)

A: Any number a can be written as , where b is any natural number. Also, 27 is a cube of 3, so 27 can…

Q: Find d

A: The given question involves the concept of modular arithmetic and the use of the modular inverse.…

Q: 7. Solve the following congruences, and check your answers: (a) x27 = 3 (mod 110) (b) x7" = 4 (mod…

A: We Know that  Definition of Congruence: If a and b are integers and m is a positive integer, then a…

Q: Question 6 Solve the following equation for x: x + 7 = 3, (mod9) A X = -4 B x = 5 x = 5, (mod 9) x =…

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Q: Define the following operation on Zn: { [1] if a = b (mod 5) [0] if a zb (mod 5) (a] * (b] = (a) Is…

A: Binary Operation : Let S be a non-empty set, then a map f : S×S →S defines a binary operation.…

Q: alculate 241100110011)s mod 7 (Note well: the exponent is given in base

A: First we convert binary number (1100110011) into decimal number. Then we use Euler phi function to…

Q: Define the following operation on Zn: S [1] if a = b (mod 5) (a] + [b] = { joj if a ±b (mod 5) %3D…

A: Consider the provided question, The provided operation on Zn is given by, a*b=1    if a≡b(mod5)0…

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

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Q: 2. Show that 1184 – 534 is divisible by 7. -

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Q: You are trying to factor n = 2288233. Suppose you discover that 8805252 = 2 ,  20572022 = 3, and…

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Q: Use the Chinese remainder theroem to find all of the soutions to x2+1=0, modulo 1313.

A: We will convert this congruence equation to a linear congruence system then we will use Chinese…