which one of the following is a congruence ? O23 = 4 mod 5 O 39 = 5 mod 5 O 39 = 10 mod 5 O 29 = 5 mod 15 O 60 = 10 mod 5

Q: The solution of the linear congruence 4x = 5(mod 9) is? 6(mod 9) 10(mod | 9) mod 9) 8(mod 9)

A: Given a statement

Q: Find the value of x in the following: 25 mod 7 =  x 8 mod 12 = x -13 mod 7 =

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

Q: ​Q3// Use Chinese theorem to solve the following congruence: X ≡ 2 mod 3 X ≡ 1 mod 5 X ≡ 2 mod 4

A:

Q: I. Solve for the smallest value of x in the following linear congruences. 1. x = 3 mod 6 and x = 4…

A: To solve given linear congruences

Q: B] Determine whether the congruence is true or false. 5 = 8 mod 3 21 = 45 mod 6 5 = 20 mod 4 100 =…

A: We have to Find

Q: 2. If x mod 5 = 4, then x could be O 571 O 400 O 633 O 719

A: Given               x(mod 5)=4

Q: 9. Let a and b be integers. Prove that if a =7 (mod 8) and b = 3 (mod 8), then: (a) a + b = 2 (mod…

A: Your questions solution below in images

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

A:

Q: Determine if the congruence is true 1. 5 ≡ 8 mod 3 2. 5 ≡ 8 mod 3 3. 21 ≡ 45 mod 6 4. 88 ≡ 5 mod…

A: We have to determine if the congruence is true.

Q: (Adapted from Richardson problem Solve the congruence 589z = 494 (mod 817). Hint: The solution…

A:

Q: Use the table in VII to give a formal proof of the following. For all integers a and b, if a = 1…

A:

Q: Which of these integers are in the congruence class of 11 mod 7? (Select all that apply.) O -11 4 6…

A: Which of these integers are in the congruence class of 11 mod 7? (Select all that apply.)

Q: Solve the following systems of congruences. a. x = 2 (mod 5) x = 3 (mod 8) b. x = 4 (mod 5) x = 2…

A: Given system of congruence are a) x≡2(mod5)    x≡3(mod8)b) x≡4(mod5)    x≡2(mod3)

Q: Let n 31 · 37. Modulo n, what is (n – 2)! congruent to? O 1 O None of the above.

A: Given:      n=31·37 modulo n

Q: 2.x = 5 (mod 3) 5x + 4 = 5 (mod 7) d.

A:

Q: Find the common solutions to the congruences 2x 3x 1 (mod 5) (mod 6) 1 (mod 7). 9 4x

A: Given : 2x≡1 (mod 5)3x≡9 (mod 6)4x≡1 (mod 7) To find : The common solutions to the congruences.

Q: Determine which of the following statements are true: a. 54=72(mod16)

A:

Q: Q7. Solve the following set of simultaneous congruences. 4x = 1(mod 5) 6x = 5(mod 11) 2x = 5(mod 13)

A:

Q: The remainder in 14 (mod 3) is 3

A: Given that 14 (mod3)

Q: 5x = 7 (mod 32)

A: To solve the following problem

Q: 2

A:

Q: The solution of the linear congruence 4x 5(mod 9) is? Qmod 9) 8(mod 9) 10(mod 9) 6(mod 9)

A:

Q: Find all solutions mod 31 to the congruence z = -5 (mod 31).

A: We will use python code to find the solutions Now x5 ≡  -5 (mod 31)  ≡  26  (mod 31) And we only…

Q: The multiplicative inverse of 52 (mod 141) O is 19(mod 141) O is 50(mod 141) O is 51(mod 141) None…

A:

Q: The solution of the linear congruence 4x = 5(mod 9) is? 6(mod 9) 10(mod 9) Qmod 9) 8(mod 9)

A: Since, x = 9 n + 8 and n element Z Now,  4x congruent 5 mod 9 implies  x congruent 8 (mod 9).

Q: 4. (a) Solve the set of congruences х 1(mod 3), x= 2(mod 4), x = 3(mod 5).

A: We  will solve it by Chinese Remainder Theorem Given  x≡1(mod3)x≡2(mod4)x≡3(mod5) Compare it with…

Q: Consider the congruence 9x   21 (mod 33). (a) Does 9 -1(mod 33) exist? Explain why or why not.

A:

Q: Use this theorem to solve the following congruences: (1) x° = 2 mod 35 (2) x' = 13 mod 35

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

Q: II. Determine whether each of these integers are congruent to 7 mod 9 4. 80 5. 106 6. -29

A: we know that x=y mod(n)  where Y is remainder

Q: Solve the following system of congruencEs. = 1 (mod 999) = 2 (mod 1001) = 3 (mod 1003) = 4 (mod…

A: Given, x≡1mod 999....(1)x≡2mod 1001...(2)x≡3mod 1003...(3)x≡4mod 1004...(4)x≡5mod 1007...(5) We…

Q: Q1 Prove or disprove i. If ac = bc(mod m), then a = b(mod m).

A:

Q: Write the set of solutions of x=5 (mod 24) x= 17 (mod 18), if any as the solutions to a single…

A: We have a set of congruence as x ≡ 5 (mod 24)x ≡ 17 (mod 18) From the first equation we can write…

Q: 25. The value of x in (7x is congruent to 12 mod 17) is O 16 15 9 13 (mod 17)

A:

Q: he solution of the linear congruence 103x = 444 (mod 999) is ) 111 ) 222 2 333 ) 444

A: We have to find x such that  103x = 444(mod 999)

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: 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: Suppose that a and b are integers, a = 4 (mod 13), and b = 9 (mod 13). Find the integer c with 0 < c…

A:

Q: I. Determine whether each of these integers are congruent to 3 mod 7. 1. 37 2. -17 3. 86

A: We will find out the required solution.

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

A:

Q: The multiplicative inverse of 103 (mod 120) * O is 7(mod 120) O None of these is 50(mod 120) is…

A:

Q: Calculate the following: 224 (mod 9) = ?

A: The expression a mod b gives the remainder obtained when a is divided by b. The reminder can be…

Q: Which of the following satisfies the congruence 4x = 1(mod 5)? O 2 O 3

A:

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

A: Properties of modulo function  a≡b(mod n ) then an≡ bn(mod n) a≡b(mod n ) then ac≡ bc(mod n)…

Q: Q3/ Use Chinese theorem to solve the following congruence: X=2 mod 3 X=1 mod 5 X 2 mod 4

A: Since you have posted a multiple question ,I will solve the first question(i.e.Q3)  for you. To get…

Q: Find a two digit integer c such that 101c = 1 mod 107. This congruence has a unique solution mod 101…

A: We need to find a digit integer c such that 101c ≡ 1 mod 107. As per the given question, this…

Q: Which of the following sets is dlosed under the given operation? O {1, 4, 5, 7} multiplication mod 9…

A: Group. Solving ques 1 According to guidelines.

Q: mod 32, given Xo=1 Please answer w

A: The congruential generator is given as:Xi+1 = 11Xi mod 32, where we are given X0 = 1. We see that,…

Q: The linear congruences a = 3 (mod 9), x = 9 (mod 24) has simultaneous unique solution modulo .…

A: The given system of linear congruence is: x≡3(mod 9)x≡9(mod 24)

Q: Find all solutions mod 31 to the congruence x° = -5 (mod 31).

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.