II. Give FIVE different answers for each of the following. 1. 49 = mod 10 2. 82 = mod 9 3. 100 = mod 21

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: . If 4x - 3 = 19 (mod 31), then the value of x (mod 31) is O 26 О 18 D 21 D 30

A: Arithmetic modulo

Q: Determine how many solutions there are for the congruence 2x= 14 (mod 16). If a solution exists,…

A: As per our company guideline we are supposed to answer only first qs, kindly post remaining qs in…

Q: Determine whether each case is true or not : * a. 44 = 13 (mod 3) > b. -55 = 5 (mod 4) → c. 74 = 1…

A: If a and b are integers and n > 0, we write a≡b(mod n) to mean n/(b-a). We read this as “a is…

Q: 5. Evaluate the following [15.17/4] = [2.11 – 17.06/3] = 34 mod 6 = 75 mod 19 =

A: The floor function x is the greatest integer function which takes as input a real number x, and…

Q: Find the value of 3443 mod 23 4 16 O 3

A:

Q: Give the least possible nonnegative solution for each of the following. 90 x (mod 11) 63 = x (mod 9)…

A: To find least positive non-negative solution?

Q: Determine which number, 0 through 6, 93 is equivalent to in modulo 7. a 93 = 3(mod 7) 93 = 4(mod 7)…

A: We want the number 93 is equivalent to in modulo 7.

Q: 16. Which of the following congruencies has NO solution? . A. 24x = 18(mod 39) B. 5x = 4(mod 10) C.…

A:

Q: 1. Which pairs of integers have a GCD of 16 and LCM of 576? a. 32 and 288 b. 48 and 192 c. 80 and 96…

A: 1)  We need to find which pairs of integers have a GCD of 16 and LCM of 576. We know that , the…

Q: 1. Solve each of the following. 14x = 1 (mod 45) 24x = 35 (mod 59) а. b. 62x = 1 (mod 99) С. d.

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Q: Consider 64z 16 mod 196. The number of solutions mod 196 is Oa None Ob 3 Oe 1

A: We find the number of solutions incongruent mod 196

Q: III. Fill-in the blanks. Tare more than 1 answer. Choose any. 1. 46 = 26 mod 2. 156 = mod 15 3. 41 =…

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

Q: One of the foll owing is not true: Oa 0= 10 mod 5 b None Oc 14=2 mod 6 Od 20 =0 mod 5 Oe -24 mod 6

A: Here we use rules of modular operation.

Q: Which one of the following is correct? a. 30 쓰 3 (mod 5) O b. 25 3 (mod 4) O c. 31 3 (mod 7) Od 20 3…

A:

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: 1. Let p be prime and let a 0 (mod p). Let b = a 2 (mod p). Show that ab = 1 (mod p). 2. Use the…

A:

Q: Determine what number the product is congruent to in mod 3. 5.8 5.8 = (mod 3 )

A:

Q: 5.4 For which primes p = 2, 3, 5, 7, 11, 13, 17, 19 is it true that a³ ≈ 6³ implies a ≈ 6 modulo p?

A: We make use of a well known result to solve the problem. The result is provided in step 2.

Q: Jump to level 1 Compute the value of -98 mod 9. Ex: 9:

A:

Q: 1. Using set notation, determine each solution set. . х %3D 1 тоd4&x 3D 1 тоd 5

A: Here questions 1,2,3 are unrelated since anyone can be solve without any help of another. So by…

Q: i need to find the value of m 12 = (m*28)mod 113

A: Solution is given by using Diophantine equation and extended Euclidean algorithm as follows

Q: 3- Find a positive integer a such that a. a-3(mod 43) b. a 7 (mod 9). c. a-13(mod 23)

A:

Q: For each pair of integers m and d, calculate m mod d. Show your work! a. m = 43 and d = 9 b. m 50…

A: If m and d be two integers . Then m mod d means that the remainder when m is divided by d .

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: Give one solution for x in each of the following statements. a. 25 x mod 5 = b. 36 x mod 8 c. 50x…

A: Please see the below picture for detailed solution.

Q: One of the following is a solution of 81x = 54 (mod 108) 43 47 45 42 has no solution

A: We are given the Equation :

Q: Suppose b is any integer. If b mod 12 = 5, what is 6b mod 12? In other words, if division of b by 12…

A:

Q: I. Find order of 5 mod m, 3 mod m, and 9 mod m J. Find a proper value for d that make the following…

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Q: Ques 3. Verify the following statements. 1. 55 - 26 = (3 - 2) (mod 4) 2. 55 - 26 = (3 - 2) (mod 4)…

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Q: . Find the value of 876,543,218,765,432,187,654,321 (mod 11) 10

A: To find the value of 876,543,218,765,432,187,654,321(mod11)

Q: Which number line represents the solution of m+ 3 < 10? A C. O A B OD 5 6 7 8 9 10 11 12 13 14 15 +…

A: The inequality :m+3&lt;10