Either solve the congruence, giving the solution as a least residue, or show that it has no solutions. 33x ≡ 21 (mod 117)

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: the number of incongruent solution of the congruence 8x = 10(mod6) is: 4. 8.

A: The given question is solved below.

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: Find a primitive root of 29 Solve x6 = 4 (mod 29)

A:

Q: (3). (a). Find all solutions to the congruence 6x = 9 (mod 45)

A: To Determine :-  All solutions to the congruence : 6x ≡ 9   mod 45 .

Q: The equation 82r = 12 (mod 13) has O 1 incongruent solution modulo 12 O 4 incongruent solutions…

A:

Q: Solve the following quadratic equation via the two different methods namely both classical and…

A: The equation a≡b mod n means that a-b is divisible by n. That is, the remainder when a-b is divided…

Q: Solve the congruency by finding the inverse: 7x = 9(mod 43)

A:

Q: For which integers c, 0<c < 30, does the congruence 12x == c (mod 30) have solutions? When there are…

A: Given congruence is 12x≡c(mod 30). We know that ax ≡b(mod m) have solutions when gcd(a,m) divides b.…

Q: Furthermore, any two solutions x and y are congruent modulo n¡n2 · Solve the following systems of…

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

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

A: Congruence

Q: The least positive integer solution for the congruence 2x = 14 (mod 18) is Answer:

A:

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: Find the four solutions of x* = 1 (mod 13).

A: Since you have asked multiple questions we will solve the first question for you .To get any…

Q: 10. (8 points) Solve 3x 2, (mod 7) or show that no solution exists.

A: Solution: The objective is to find the solutions of 3x≡2 (mod 7)

Q: . (a) How many quadratic residues are in the residue set Z19? (b) Determine if 4 and 9 are quadratic…

A: Introduction: Quadratic residue is a part of congruent modulo theory. It is a non-linear congruence.…

Q: The liñear congruence 9x = 19 (mod27) has 3 incongruent solutions. :Select one True False

A:

Q: Solve each equation for x.  5x ≡ 2, (mod 7), x, (mod 7) 7x + 1 ≡ 4, (mod 11), x, (mod 11)

A:

Q: solve the quadratic congruence 7x^2 - 8x +4 = 0 (mod 17)

A: The given problem is to solve the given quadratic congruence equation 7x2-8x+4 = 0(mod 17)

Q: 6. Solve the equation x + 3x + 17 = 0 (mod 21)

A: The Chinese reminder theorem:                    Let p and q are coprime. Then the system equations…

Q: 3. First solve for q: (a) 143 = 1( mod 2) (b) Rewrite 143 as the product of 11 x 13 and show that…

A: Consider the given information: a=q m+ r Where a= dividend , q=quotient, m=mod , and r=remainder. To…

Q: he linear congruence 132x = 76 (mod 100) has a solution. elect one: D True D False

A: I will use the property of linear congruence relation.

Q: Solve the congruence: 341x ≡ 2941 (mod 9).

A:

Q: 6. Find all incongruent solutions to each congruence. Show your steps. (a) 135x = 108 (mod 612) (b)…

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Q: The linear congruence 9x = 19 (mod27) has 3 incongruent solutions. :Select one True False

A:

Q: Solve the congruence: 6x ≡ 4 (mod10)

A: The congruence could be written as,

Q: the number of incongruent solution of the congruence 8x = 10(mod6) is:

A:

Q: The equation 15x=30 (mod 50) has: 5 non-congruent solutions modulo 50 6 non-congruent solutions…

A:

Q: How do I use the Chinese Remainder Thm to solve this system of congrunces below? x ≡ 1 (mod 3) x ≡ 4…

A:

Q: X=1 (mod 81) and X = 7 (mod 12), as the solutions to a single congruence.

A: It is given that X=1mod81 and X=7(mod12) Here a1=1,a2=7,n1=81,n2=12 Therefore:…

Q: 24. Given the linear congruence (16x is congruent to 72 mod 24.) How many possible incongruent…

A: 24. To find the number of incongruent solutions of16x≡72mod 24

Q: Solve the congruence x² = 9 (mod 600).

A: Given congruence is x2≡9 mod 600

Q: Find all solutions to the congruence13x−3 = 4 (mod 26). If none exists, explain why.Your…

A:

Q: 3

A:

Q: solve by means of a derivation, the congrucnce equation; 10x= 4 (mod 2a) Express ansurer in form X=…

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Q: the number of incongruent solution of the congruence 8x = 10(mod6) is: 2) 8. 4

A:

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: Number theory

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: Does ?2 ≡ 23 (mod 79) have any solutions. Justify your answer using the Legendre symbol.

A: Note that the congruence X^2= 23 (mod 79) will have solution if and only if 23 is a quadratic…

Q: c. Find all non-congruent solutions to x? = 1 (mod 15) d. Find all non-congruent solutions to x2 = 4…

A:

Q: Use the repeated squaring method to calculate the following: 16^10 (mod 230)

A:

Q: The equation 12x=24 (mod 48) has:

A: ANSWER IS 12 NON  CONGRUENT SOLUTIONS MODULO 48

Q: x = 13 (mod 39) have a solution. Select one: O True 2.

A: True

Q: 10. Solve the following modular congruences or show that there is no solution. (^) 10r =1 (mod 31)…

A: We will find out the required value.

Q: The number of mutually incongruent solution(s) of 307x = 83 (mod 360)

A: BY THE DEFINITION OF Modulus congruence Modulus congruence means that both numbers, 16 and 21 for…

Q: Solve for a a ≡ 13 mod 5353

A: To solve  a ≡ 13 mod 5353

Q: Ф(тk) — ф(0) — тk

A:

Q: Which of the following is a solution of congruence equation, 4x –7 =3 (mod 10)?

A: We will find out the required solution.

Q: Solve the Diophantine equation 7x + 5y = 43 by  rst solving the congruence 7x = 43 (mod 5), which is…

A: