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

Q: What is the number of solutions to the congruence in Z125? x³ + x² + 3 = 0 (mod 125)

A: As per the question we have to solve the following polynomial congruence equation : x3 + x2 + 3 ≡ 0…

Q: Solve the linear congruence 7x = 13 (mod 19).

A:

Q: The equation 20x=30 (mod 70) has: 10 non-congruent solutions modulo 70 None of these no solution…

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: Solve for x: 7x = 3 mod 11

A:

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

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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: 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: (i)Find the inverse of 5(mod9)     (  ii)Hence or otherwise solve simaltaneous equation…

A:

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

A: Congruence

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

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

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

A:

Q: Given a = 4( mod 9) and b = 5( mod 9), find c with 0<c<9 such that c = 5a + 3b ( mod 9)

A:

Q: Does x2 +3x+7=0 mod 31 have solutions? IF

A: This follows in the same way as we study quadratic equations. Here we use facts about quadratic…

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

A: Linear congruence

Q: (a) Find two integers satisfying the equation r³ + 24x² – 2 = 0 mod 23.

A:

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: The equation 21x=49 (mod 70) has: 6 non-congruent solutions modulo 70 7 non-congruent solutions…

A:

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: i need to find the value of m 12 = (m*28)mod 113

A: Solution is given by using Diophantine equation and extended Euclidean algorithm as follows

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

A:

Q: X = 17 (mod 21) X= - ) 8 Cmod 25

A:

Q: Does x2 + 5x congruent to 12 (mod 31) have a solution? (Hint: complete the square)

A:

Q: the number of incongruent solution of the congruence 8x = 10(mod6) is: 1. 4 2) 8)

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

A: The congruence could be written as,

Q: Number theory

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

A:

Q: Find the value of x if any. Show your complete solution. 1.   (13 + x) = 3 mod 16 x = 2.   (3x +…

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Q: Does 5x = 6 mod 12 have a solution? How many?

A: As per our guidelines we are supposed to answer only One question  if there are multiple questions…

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

A:

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: b. 3x = 0 (mod 21)

A:

Q: or what values of k, x=4 will be a solution for 3x²+4x = k mod31?

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: Find the mod of (2-4i)^1/2

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Q: Number theory

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Q: . Find a solution x € Z, 0 <x <n, for the congruence 57x + 7 = 78 (mod 53).

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: Does

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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: 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: (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: 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: 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…

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Q: solve the following congruence equation:3x+58 ≡1(mod 12)

A: If ab≡bc(mod nb) then a≡c(mod n) And if ab≡bc(mod n) and if (b,n)=1 then a≡c(mod n)

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.