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

Q: 8. Solve the following congruences. a. 5x + 3 = 13 (mod 14) b. 4x = 20 (mod 8)

A:

Q: Find the solution to 34x = 77(mod 89) that is positive and less than 89.

A: given that                                          34x≡77 (mod 89) we have to find positive…

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: Suppose b is any integer. If b mod 12 = 7, what is 8b mod 12? In other words, if division of b by 12…

A: Given b mod 12= 7  To find 8b mod 12

Q: Perform the following calculations. a. (14 + 30) mod 19 b. (14-30) mod 19 C. (3*13) mod 19

A: To perform the given calculations we shall use the following rules…

Q: V. Suppose that a and b are integers, a = 7 (mod 19), and b = 5 (mod 19). Find the integer c with 0…

A:

Q: x is congruent to 43 mod 12. Then x is

A: x is congruent to 43 mod 12 implies x congruent 7 (mod 12). So, solution in the least residue system…

Q: (1) Consider the equation 2.x +1 = 0 mod n. For which n are there no solutions? one solution?…

A: Congruence

Q: 1. Solve each of the folling. а. с. d. 115x = 2 (mod 288) 2. Explain why 12x = 1 (mod 75) has no…

A:

Q: 1. Find the value for q given: (a) 39 = 4( mod 5) (b) -43 = 1( mod 4)

A: Note: Hi! Thank you the question, As per the honor code, we'll answer the first question since the…

Q: The integer solution of the 2x³ + 7x – 4 = 0(mod 5), then а) х—4(тod 25) b) x = 1(mod 5) c) x =…

A: Congruence

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

A:

Q: 5x = 7 (mod 32)

A: To solve the following problem

Q: 3. Solve each of the following congruences. (a) 6x + 3 = 4 mod 10 (b) 6x + 3 = 1 mod 10 (c) x² = 1…

A:

Q: 22. Suppose c is an integer. If c mod 15 = 3, what is 10c mod 15? In other words, if division of c…

A:

Q: #5. Suppose that a = 2 (mod 113), and b = 5 (mod 113) What is (a b + 56b + 155) mod 113?

A: given a≡2(mod113),b=5(mod113)a3≡23(mod113)a3b≡235(mod113)56b≡280(mod113)56b≡54(mod113)155≡15mod113)

Q: V. Suppose that a and b are integers, a = 7 (mod 19), and b = 5 (mod 19). Find the integer c with 0…

A:

Q: The last two digits of 52044 is 44. If ab = 0 (mod 3), then a = 0 (mod 3) or b = 0 (mod 3). F 10. F…

A:

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: For all integers a and b, if a = 7 ( mod 8)and b = 3 ( mod 8), then (a + b) = 2( mod 8).

A:

Q: Which of the following are true modulo 12? (1) Does 5z = 6 mod 12 have a solution? How many? (2)…

A:

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: Q7. Solve the following set of simultaneous congruences. 6x = 1(mod 5) 5x = 3(mod 11) 2x = 5(mod 13)

A:

Q: Suppose that a and b are integers, c b = 3 (mod 19). Find the integer c that a) с%3D 13а (mod 19).…

A:

Q: Consider the equation 2x + 1 = 0 mod n. For which n are there no solutions? one solution? multiple…

A:

Q: -) Find the solutions, if any, of each congruence. 21x 10 (mod 35) 9x = 15 (mod 21).

A: We know that, ax≡b mod n has solution if and only if gcd(a,n) divides b.

Q: Suppose b is any integer. If b mod 12 = 7, what is 5b mod 12? In other words, if division of b by 12…

A:

Q: which one will give a solution of [6,13] a)4x is identical to 3 mod 7 b)9x is identical to 11 mod…

A: which one will give a solution of [6,13]

Q: The order of 5 mod 17 is

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

Q: The order of 5 mod 17 is *

A: Since ϕ(17) = 16 Therefore order can be the divisor of 16 So the order can be 1,2,4,8 or 16

Q: Solve the following congruence equations. 1. x=2 mod 3 2. 9x = 21 mod 30 3. 18x = 30 mod 42

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

Q: Find all possible positive values of m: 47 = m mod (5)

A:

Q: 1. x=2 mod 3 2. 9x = 21 mod 30

A:

Q: Find an integer x that satisfies the equation. 5* = 4(mod 11) 17x?=10(mod 29) i. %3D ii.

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Q: A sequence of pseudorandom numbers is generated as follows Xo = 4 x₁ = ( 6x₁-1 + 5 ) mod 13 if i > 0…

A:

Q: Which of the following is false? a. (x-y+2) = (x-y-11) (mod13) b. (x-y+2) = (x-y-32) (mod 17) c.…

A: Sol:- Check each statement:- a.x-y+2≅x-y-11mod 13Since, 2 mod 13 = -11 , This statement is…

Q: 3. If x mod 4 = 1 and y mod 4 = 3, then xy could be O 901 O 299 O 508 O 113

A: We shall use the division algorithm

Q: 4. Solve the following: 34x 60 (mod98) 5. Detemine all the possible positive m values greater than 1…

A:

Q: Deduce the following statements: i) an odd prime number p is the sum of two squares of integers if…

A:

Q: Find the whole number of (3+12) =7 mod 10

A: The given equation (3x+12) ≡7 mod 10. Consider the following congruence equation (3x+12) ≡7 mod 10.…

Q: III. Determine the value of a such that: 7. a = 20 mod 27 and -26saso 8. a = 20 (mod 31) and -15 < a…

A: Please check step 2 for the solution.!

Q: Which is the solution of 71x congruent to 5 mod 142. 38 57 85 None of the above

A: To determine which of the given is the solution of 71x≡5mod142.

Q: 3. Find a solution to the following systems, if possible. a) X = 2 (mod 21) and X = 3 (mod 91) b) 2X…

A: Find the solution

Q: 8. a = 20 (mod 31) and -15 s as 15.

A: As per the guidelines I am supposed to answer the first question only . For the other questions…

Q: 10. Find the sum of all incongruent solutions of a =1 (mod 17). (Enter the least non-negative…

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Q: 2222 (mod 13) is equal to 12 (mod 13) 2 (mod 13) None of the mentioned 6 (mod 13) 1 (mod 13)

A:

Q: The equation 12x=24 (mod 48) has: O 24 non-congruent solutions modulo 48 6 non-congruent solutions…

A: To find- The number of solutions for the given equation.

Q: Calculate (13, 000 +2)10 (mod 13). Find the omeir lor of 3456 whon dlivided by the following Hint:…

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Q: Answer each of the following questions. V ? 1. 23 = 56 mod 4 True 2. 24 = 154 mod 13 False 3. –4 = 4…

A: