The quadratic congruence x^2+4x+1=0 mod 7 is solvable True False

Q: (a) Solve the linear congruence 26x = 1 modulo 33

A: Solution

Q: Prove that Master Cheng has won precisely 21 times in a row during some consecutive days.

A: Please find the solution

Q: Solve for x: 7x = 3 mod 11

A:

Q: x^2 ≡ 1 (mod 105)

A: Given: x2≡1(mod 105) To Solve: The given congruence  x2≡1(mod 105)

Q: Find all whole number solutions of the congruence equation.  2x+1≡ 5 mod 4 3x+1≡ 4 mod 9

A: The given problem is to find the whole number solutions for given system of linear congruence…

Q: 6) find all the and non residues (mods) incongruent quadratic residues

A: It is given that Incongurant quadratic residues.

Q: Solve the system of congruence's by using Chinese Remainder Theorem x =1 (mod 5) x =2 (mod 6) x = 3…

A: Consider the given information. x≡1 mod5x≡2 mod 6x≡3 mod 7 The general form of congruence is defined…

Q: What is the smallest integer that is a quadratic residue for all prime moduli p > 2?

A: We know if there is an integer 0<x<p, where p is a prime, such that x2≡qmod p, then q is said…

Q: 6) find all the incongrunt quadratic residues aned non residues (mods)

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

Q: 2X=3 mod 5 Show your work

A: the given congruence equation is 2x≡3mod 5 the general congruence equation is ax≡bmod c…

Q: Find all the primitive roots modulo 125.

A:

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

A:

Q: Prove that all generators of Z20 are prime numbers. Please provide complete solutions. Thank you.

A: The statement is incorrect as 9 is generator of Z20, but 9 is not prime number.

Q: 3. Solve the system of congruences x = 1(mod 5) x 2(mod 6) r= 3(mod 7)

A:

Q: Use the index system modulo 19 to find all solutions of x3≡11(mod 19) and 5x≡4(mod 19).

A: The congruences given are as follows: x3≡11mod 195x≡4mod 19 We are asked to find the value of x that…

Q: 5. Explain why the congruence r = 2 (mod 4) has no solutions in Z.

A: We have to show that the congruence x2≡2(mod 4) has no solution in ℤ

Q: Solve for x : 5x ≡ 7 (mod 6).

A: Here remainder is 7 and modulus is 6 we can write it as  5x-7 =6n          Where  is an positive…

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: Solve the congruence3x−7 = 2 (mod 16). Your solution should be positive and reduced modulo16.

A:

Q: 2. Find all solutions of the linear congruence 12x = 9 (mod 15).

A: P

Q: solve for x^2 = 1 mod 8 and x^2 = 1 mod 10

A: Solution...

Q: Find all the non-congruent solutions to  4x ≡ 6(mod 21)  express solutions using the stand…

A: Introduction: A linear congruence is generalized as ax≡bmod n. The greatest common divisor of a and…

Q: What is 2 ^32 mod (5)?

A: mod is the function whose output is always positive. mod is represented by .

Q: Solve the system of congruence x ≡ 3(mod6) and x ≡ 4(mod7) using the method of back substitution.

A: System of congruence equations

Q: Find all whole number solutions of the congruence equation. (2x + 1) ≡ 5 mod 4

A: Consider the given congruence equation. (2x + 1) ≡ 5 mod 4

Q: Show that 18! ≡ -1 (mod 437).

A: We have to show that: 18!≡-1mod437

Q: 11. Solve the congruence 4x = 5 (mod 9).

A:

Q: Solve x2+3x+2 is congruent to 0 (mod 55)

A: 55=5×11 and gcd(5,11)=1, hence they are co-prime.The given system of equation x2+3x+2≡0mod 55 is…

Q: Find the solutions of the congruence 15z + 19x = 5 (mod 11)

A: This question is related to Number Theory

Q: What sequence of pseudorandom numbers is generated using the linear congruential generator Xn+1 =…

A: Given that xn+1=(3xn+465)mod 8191x0=1

Q: Find the smallest positive integer satisfying the system of congruences: x ≡ 1 (mod 3) x ≡ 2 (mod…

A: Here we will find out the required value.

Q: 2x ≡ 12 mod 5 5x + 4 ≡ 2 mod 8

A: 1) 2x = 12 mod 5  2x = (5*2 + 2) mod 5  2x = 2  x = 1  (1 is whole number)    Only 1 whole number…

Q: Solve by using the Chinese remainder theorem for the congruence X 2 (mod 7) X 4 (mod 5)

A: Given that This can be written as,

Q: Compute all least residue solutions modulo 12 of 8x-4 congruent to 0(mod 12)

A:

Q: What sequence of pseudorandom numbers is generated using the linear congruential generator xn+1 =…

A: According to the given information, it is required to find the sequence of pseudorandom numbers.

Q: Only 1 of the next 10 COVID-19 patients will recover. All of the next 10 COVID-19 patients will…

A: Here given that fatality rate of covid 19 here in the Philippines up to date is 1.6%   P =…

Q: 25 Prove that mod 7 5 for all Gindegars and bin b mod 7-6

A:

Q: What sequence of pseudorandom numbers is generated using the linear congruential generator xn+1…

A: Determine the sequence of pseudorandom numbers generated using the linear congruential generator…

Q: Find all solutions of quadratic congruence x^2+85x+2=0(mod401)

A: We follow the method of completing the squares of the equation x^2+85x+2. Note that 85 is odd so we…

Q: 6. What sequence of pseudorandom numbers is gener- ated using the linear congruential generator xn+1…

A: Given: Linear congruential generator xn+1=4xn+1 mod 7, with x0=3 To find: Sequence of psedorandom…

Q: Solve the system of congruences 2x + 6y = 3 (mod 15) 3x + 7y = 6 (mod 15)

A:

Q: Number of solutions for the congruence equation x^2 + 2x + 1 = 0(mod 52) is

A: The given congruence equation is x2+2x+1 = 0(mod 52)

Q: Solve the system of congruence's by using Chinese Remainder theorem x = 2 (mod 5 ) x = 3 (mod 7) x =…

A:

Q: 6. Show that Autoq(Q[3], 5]) is finite.

A: To show: Autℚℚ35,53 is finite.

Q: Solve the linear congruence 5x = 3 (mod. 11). (Show all the work.)

A: The expression, a≡b (mod c)  implies that c divides a-b, that is when c divides a-b the remainder is…

Q: Give an example of a pair of numbers that can be used to generate modulo residues to represent the…

A:

Q: The system  x ≡ 2 (mod10)  x ≡ 7 (mod15) is solvable Select one: True False

A: The system  x ≡ 2 (mod10)  x ≡ 7 (mod15) is solvable Select one: True False

Q: Use Fermat’s little theorem to find the least residue of 863 modulo 31.

A: Fermat's little theorem says: ap≡p(mod p)gcd(a,p)=1

Q: (b) Solve the set of congruences 2x =1 (mod 5) x=3 (mod 4)

A: Note:- We’ll answer the first question according our protocol. Please submit a new question…

Q: 12x ≡ 18 (mod 15) has exactly 3 distinct solutions modulo 15 Select one: True False

A: 12x ≡ 18 (mod 15) has exactly 3 distinct solutions modulo 15 Select one: True False

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.