Find an integer x satisfying the equation: 4x21 = 2(mod 5) or show that no such integer exists.

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: find x, where x= 9753 (mod 120) and -120<x<0

A: Ans: -87

Q: Express each nonnegative integer a less than 15 as a pair (a mod 3, a mod 5).

A: The values of a could be, 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14.

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

A:

Q: Find all solutions of the congruence x2 ≡ 29 (mod 35).

A:

Q: just give the handwritten solution. Solve the congruence: 7x^5 congruent to 6(mod 17)

A: The solution is given below

Q: Either solve the congruence, giving the solution as a least residue, or show that it has no…

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: 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: For this question, explain the reason if no solution exists. Give a complete list of solutions if…

A:

Q: Find the primitive roots (mod 17).

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: (a) Solve for x if 25x = 15(mod 29).

A: Linear congruence

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 equation 5x = 13 (mod 18)

A: Given: To solve: the equation 5x4≡13mod 18Formula: a≡bmod cis equivalent to saying by Euclid's…

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: Find an integer A so that: A79 = 7 (mod 277) Please solve step by step thanks!

A: Given an equation. Let's solve for A.

Q: Solve the congruence x² +1 = 0 mod 13°.

A:

Q: Use Hensel Lifting (twice) to find a solution to x² = 7 (mod 374).

A: According to the given information, it is required to use Hensel lifting method to find the…

Q: b) Determine whether or not x? = 85 (mod 97) has a solution.

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: Suppose that a and b are integers, a = 4(mod 13), and b = 9(mod 13). Find the integer c with 0<c< 12…

A: We will use the basic properties of congruence modulo n relation to answer this question.

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: Using Fermat's theorem, find 3201 mod 11.

A: Euler's Theorem states that for any natural  number n, we  have  aϕ(n)≡1(mod n) where ϕ(n) denotes…

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

A: Given congruence is x2≡9 mod 600

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: Find all solutions of x = 10 (mod 133).

A: A congruence of the form, f(x)≡0(modm), where f(x)=anxn+an-1xn-1+...+a1x+a0, ai=0,1,2,...,n is…

Q: Give all non-negative solutions for 10r =-17 mod 4.

A:

Q: Find the nonnegative integer a less than 28 represented by each of these pairs, where each pair…

A: According to the given information, it is required to find the non-negative integer a less than 28…

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

A: First Option Is Correct Answer.

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

A:

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

A: The given equation is 82x = 12(mod 13)

Q: In(n² = n(mod 10)), domain is the set of positive integers.

A:

Q: Number theory

A:

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

A:

Q: Find all solutions of 3* = 17 (mod 224)

A:

Q: Find, with proof, all primitive roots mod 27.

A: To find all primitive roots mod 27,

Q: Does

A:

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: Either solve the congruence, giving the solution as a least residue, or show that it has no…

A: We will check whether the given system of congruence has solution or not.

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: (a) Find an integer r E {0,..., 196} which solves the equation 167 = 7 (mod 197).

A: Given equation is x157≡7mod197. We have to find that an integer x∈0,....,196 which solves the…

Q: Solve for a a ≡ 13 mod 5353

A: To solve  a ≡ 13 mod 5353

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

A: We will find out the required solution.