SImalest posiuiy OI the n) is order of a modulo n. Find the additive orders of each of the following elements by solving the appropriate congruences: (a) 7 modulo 11. (b) 9 modulo 15. (c) 8 modulo 15.

Q: 46. Find the order of 7 modulo 172.

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Q: if b is modulo m and a is another unit with a=b mod m, we say that d is the---------of a modulo m to…

A: As with such a large amount of concepts we are going to see, congruence is straightforward, perhaps…

Q: For n, ke Z, k0, we denote by A(n, k) the set of integers that are congruent to n modulo k: -2k+n,…

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Q: (7) (a) Find the order of a modulo 7 for a = 1, 2, 3, 4, 5, 6.

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Q: perform the calculation in mod 7 a. [18]+[25] b. [5][8]

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Q: Let x be an integer coprime to 1450 that is not congruent to 1 modulo 1450. Suppose we know that x1…

A: The given two MCQs are exactly same. Hence we will just solve the first one. And we will use the…

Q: Q// Let m = 5, 1- Write the Addition table (Cayley's Table). 2- Write the congruence classes of…

A: For m=5 , our set is Z5 .

Q: Let a and b be integers satisfying a=3(mod 11) and b=8 (mod 11). If c=3a+4b then None of these c=9…

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Q: Let P(n) be the assertion that: for any integer n 2 1, 7" - 1 is divisible by 6. Part 1 Part 2. In…

A: Principle of Mathematical Induction :Let P(n) be a statement .step 1 : For n=1 is true .step 2 : Let…

Q: You are trying to factor n = 31831 which happens to be the product of 2 primes. Suppose your tions.…

A: An effective way to determine the greatest common divisor (GCD) of two integers is to use the…

Q: Let n = 17. Sha

A: Given: Value of a, b, n. We have to check whether a≡b mod n    or   a≢b mod n.

Q: What are the values of d so that 15(mod d ) = 3?      A. d = {4, 6, 12} B. d = {8, 12, 24} C. d =…

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Q: (a) 55 mod 7. (b) –101 div 3.

A: (a) 55 mod 7  As 55 = 7•7+6 So that  55 mod 7 = 6 mod 7

Q: Test2

A: We know that2198=2128×264×24×22Also we have22≡4(mod 397)24≡16(mod 397)28≡256(mod…

Q: Prove the given statement of divisibility of 13 Divisibility of 13 Method 1:              Step 1:…

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Q: Number 1 only

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Q: explain please

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Q: If x98 = 1(mod 97) then possible value of x is of (a) 97 (b) 194 (c) 90 (d) 291 (е) None of these O…

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Q: Thearem: P is a prime number; a is a integer i Let la,6) be a pacitive integer, In this cose; ond…

A: In this,using theorm,here p- prime,a - integer (a,b)=1,n is a integer. Here x^n=a(mod p)congruence…

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

A: Introduction: Bezout's Theorem, also known as Bezout's Identity, is a fundamental result in number…

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

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Q: g) Determine the product of Factorial of 5 and Fibonacci of 5 using the recursive function as…

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Q: Inverse of 9 modulo 23 is -18 -17 18 17 Windows by

A: Solution: We have to find the inverse of 9 modulo 23. Let x be the required inverse. Then, 9x≡1mod…

Q: True or False. Briefly explain why.  The least nonnegative residue of −123 modulo 12 is 3.

A: We recall the definition.

Q: Is 7|(15+20): True or False? 28 is congruent to 42 modulo 6: True or False?

A: I am solving these in step 2

Q: What is the order of 3 modulo 101? Is 3 a primitive root modulo 101?

A: Here we have to find the order of 3 modulo 101 and find if 3 is the primitive root modulo 101 or…

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: Ti If a = b (mod n) and b =c (mod n) then which of the following is true. (a) a = c (mod n) (b) a2 =…

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Q: If a = 1 (mod n) and b = 1 (mod n) then a - b = 0 (mod n) اختر واحدا: 2 3

A: True.

Q: 5. Find the highest power of 2 that divides each of the following integers. a) (101111110)2 b)…

A: Given: (101111110)2 (1010000011)2 (111000000)2 (1011011101)2 Which of these is divisible by 3

Q: In each computation, find the unique r such that a ≡ r(mod n) with 0 <= r < n.  (d) (10)2022 ≡ r…

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Q: Find oll integers Such thot 24! x =1 Cmod 2) 5x = 3. (mod 8) and 1500 < X <2000

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Q: Hanb(mod n) and b c(mod n) then which of the following is trae. (a) anc (mod n) () 2=c(mod n) (c)…

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Q: Given 101 is a prime number. Then (100101 – 9101 + 3200)(mod 101) = 92(mod 101) None of these 94(mod…

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Q: 5. Find an integer x between 0 and 776 such that x 13 (mod 21) x = 5 (mod 37)

A: Set N = 21 × 37 = 777. Then , m1  = N/21 = 777/21 = 37 and m2 = N/37 = 777/37 = 21 Now we need to…

Q: Number theory TOP 3 ONLY!!!

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Q: Let p = 31 (a) How many primitive roots are there mod 31? (b) Is 2 a primitive root? Explain. (c) Is…

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Q: True or False. Briefly explain why.  {−13, −6, −3, 1, 10} is a complete residue system modulo 5.

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Q: Which of the following is valid congruence Modulo n? Select one: O a. None of them ОБ. 12 (-5тod3) O…

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Q: A Password consists a list (order counts) of symbols. Beulah makes a password from 2 different…

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Q: किस्) dn - 2 1h cm n is. 1-1 1- of these 111 none

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Q: USING MODULAR ARITHMETIC PERFORM THE FOLLOWING OPERATIONS    A).  (27 + 7) (mod 4)…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

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