Which of the numbers listed below are congruent to 4 modulo 3? Select ALL that apply. 0-2 02 03 04 Submit Question Calculate the following. (a) 37 +2 100% = (b) 10, 249 10 3, 547 = Submit Question of

Q: Find each of the following, fully justify your claims. (a) Suppose that n div m = 2021 and that n…

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

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Q: Least residue of 8^68 modulo 17

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Q: 6. Working modulo 9 or 11, find the missing digits in the calculations below: (b) 2r99561 = [3(523…

A: To find- Working modulo 9 or 11, find the missing digits in the calculations below: 2x99561 = 3523 +…

Q: If today is Thursday, what day of the week will it be 20 days from now? Friday O Monday O Thursday O…

A: Introduction: For two given integers a and n, either n divides a or n doesn't divide a. When, n…

Q: I. Determine the value of b in a = b mod m when: 1. a = 225, m = 119 2. a = 9000, m = 223 3. a =…

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Q: A. Find the value of x. 61 = x ( mod 7) 1. 71 = x ( mod 8) 2. 5) 89 = (x + 3) ( mod 4) 78 + x = 3 (…

A: The given equation are: 1. 61≡xmod 7 2. 71≡xmod 8 3. 78+x≡3mod 5 4. 89≡x+3mod 4 Calculate the value…

Q: 1. Let a be a prime number. Suppose that a=0 mod 29. Determine the value of a. Prov that your answer…

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Q: Evaluate (3459874 * 457832 * 34568) mod 10. Box in your final answer. Remember to show all work.

A: As we know  a*b mod n = (a mod n)*(b mod n)

Q: Use permutations to solve. From a cooler with 6 different kinds of soda, 4 are selected for 4…

A: nPr = n!/(n-r)!

Q: 6. Homework. Find the inverse of 356 (mod 678119). Hint: Solve for z in 356r 1 (mod 678119), where r…

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Q: a. Find an inverse for 210 modulo 13. b. Find appositive inverse for 210 modulo 13. c. Find a…

A: a) To find an inverse for 210 modulo 13. b) To find a positive inverse for 210 modulo 13. c) To find…

Q: Find the value of 786 (mod 13) using Fermat's Little Theorem. Remember, x (P - 1) = 1 (mod p) 786 =…

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Q: (H2) Determine the number of integers n < 1000 that have primitive element modulo n. a

A: Solution: We will use the following fact: The only numbers that admit a primitive root are those of…

Q: Find the remainder of 1111^2222+2222^3333+3333^4444+4444^5555 modulo 17

A: We have to find the remainder of 11112222+22223333+33334444+4444555517 Firstly we take 1111222217 if…

Q: 14. The expression "a mod b" is used to mean "the remainder obtained when a is divided by b". Which…

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Q: 8. Use Euler's Theorem to find a number a between 0 and 9 such that a is congruent to 7 1000 modulo…

A: We know according to  Euler's Theorem  that  xϕ(n)≡1(mod n) where the function ϕ(n) counts the…

Q: 2. Create the following tables: (a) Addition table for modulo 7 (b) Multiplication table for modulo…

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Q: Determine how many ti (o bom is a prime.

A: In this question, the number of times is determined when 1 appears in the multiplication table for…

Q: Suppose you are using the fast method to compute xe mod N, where x=23, e=101 and N=515. You have…

A: We will find out the required value.

Q: 4. x = 2 (mod6) x = 5 (mod⁹) x = 8 (mod11) x = 11 (mod15)

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Q: - Show that (a + b)" = a + bn mod 2 for all integers a, b, and n with n > 0. Hint: Try looking at…

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Q: 100 nd a number between 0 and 12 that is congruent to 2"modulo 13. Show your work.

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Q: Find a formula for the general term a, {5, 8, 11, 14, 17, .} 5n + 3 On+3 O 3n + 2 O 2n + 3

A: We can answer the question as below

Q: divisionless mod" where x mod y is computed in steps. One step is to consider y in the form of 2a -…

A: I have answered this question in step 2.

Q: modulo them? For which of the following prime numbers are 2 a square 59, 61. 17, 19,

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Q: Find the order of 4 modulo 49.

A: We have to find the order of 4 in the group of multiplication modulo 49. The order of 4 is the…

Q: the given values of n=9 and a=69, find the number b∈{0,1,…,n−1} for which a≡b(mod n

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Q: Find the order of 4 modulo 49.

A: Evaluate order of 4 modulo 49.

Q: 3. The Lucas Lehmer Test is applied below to test whether the number 255 is prime or not. (S,' -2 k…

A: The Lucas Lehmer test: Let Mp =2p-1  be the Mersenne number to test where p is an odd prime.…

Q: what is the particular solution to the difterential equahion y's +e, subject to y l) = 4e %3D why…

A: Given differential equation is y'=-yx+ex we can write it as y'+yx=ex I.F. is I.F.=e∫1xdx=elogx=x…

Q: One step is to consider y in the form of 2a - b. When y is 125, what are a and b? Find: A = ? B =…

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Q: Using the digits 0 through 8, find the number of different 5-digit numbers such that: (ANSWER…

A: While selecting the cases if the order of the selection matters then it is considered as permutation…

Q: 30. Find the integer a such that a) a = 43 (mod 23) and -22 < a s0. b) a = 17 (mod 29) and -14 < a s…

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Q: The inverse of 3 modulo 7is -2 0 صواب İhi O

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Q: JESTION 2 The prime number 8191 is a Inverse of 7 modulo 11 Carmichael nmber Mersenne prime mmber…

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Q: The annual interest rate on a credit card is 12.99​%. If a payment of ​$200.00 is made each​ month,…

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Q: ere they want me to find a div m and a mod m when a = −33, m = 67. How I solved, I divided -33 into…

A: To find a div m and a mod m when a = −33, m = 67. Given information:  a = -33 m = 67

Q: on 10 of 16 25628 49977 376? Find the missing number? O A) 40 O B) 38 OC) 39 O D) 35

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Q: 5. Find the last digit of 6. Find the last digit of the decimal expansion of 799.9. noritive residue…

A: We need to find the last digit of the decimal expansion of 7999,999.

Q: Find the order of 5 modulo 31.

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Q: Q#5. The United States Postal Service (USPS) sells money orders identified by an 11-digit number…

A: The 11-digit number is x1.x2.....x1111th digit satisfies x11=x1+x2+....+x10mod9

Q: Q1: Give suitable response to the followings. a) ndexed Family b) Mathematical Induction c) Indexing…

A: Since you have posted a question with multiple sub-parts, I will solve the first three subparts for…

Q: N is a positive integer such that 53263 mod N = 7. What is the value of (532632 + 5) mod N. (You can…

A: See the detailed solution below.

Q: a) Find a, b if a + 2b = 116 mod 9 and 2a + b = -62 mod 7. b) Write the prime factorization of…

A: Note: We are allowed to solve one question/ three subparts at a time so kindly upload remaining…

Q: Decimals can be approximated by using only the leading nonzero digit or by rounding to the leading…

A: Answer : Approximate 0.0081 by using the leading nonzero digit = 8.1 × 10-3

Q: 5) If p is an odd prime, then 2(p – 3)! = ?? (mod p) a) 2 b) 1 c) - 1 d) - 2

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Q: Find 3 values of n such that phi(n)= 120

A: According to the given information, it is required to determine the values of n such that:

Q: 5. Show that (a + b)n = a + bn mod 2 for all integers a, b, and n with n > 0. Hint: Try looking at…

A: Given data: (a-b)n= an +bn mod 2 for all intergers a,b and n with n&gt;0.

Q: 5. Working modulo 9 or 11, find the missing digits in the calculations below: (a) 51840 273581 =…

A: The solution is given below