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

Q: Solve the quadratic congruence, 6x²-7x+2 ≡ 0 mod 31.

A: We have to solve the above quadratic congurence.

Q: 7x = 4 (mod 12).

A:

Q: ions of the congruence 15x^2 + 19

A: Given:- 15x2+19x≡5 mod 55

Q: 4x=22(mod10)

A:

Q: Prove that 1+1=2

A: To prove: 1 + 1 = 2

Q: Solve the system 3x + 2y = 5 2x + 7y= 9 mod 17 mod 17

A:

Q: Which of the following linear congruence has 1 incongruent solution? (a) 3x = 9 (mod21) (b) 14x = 12…

A: The solution is given as

Q: Find all solutions to the following quadratic congruences by first making the leading coefficient 1…

A: Topic:- algebra

Q: Solve the following quadratic congruences: (a) 3x² + 9x + 7 = 0 (mod 13) (b) 5x² + 6x + 1 = 0 (mod…

A: According to Q&A guidelines, I can answer only one question. So I answered (a).

Q: Show that x2 + 9 is prime.

A: To show x2 + 9 is prime.

Q: x3-3x2+27 is congruent to 0 (mod 225)

A: Consider the following problem  x3-3x2+27≡0mod 225 Prime factorization of 225 is 32×52 Now,…

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: 2x² – 3x = 9(mod13) X = (mod13)

A:

Q: 7. If aatiß = (x + iyy*4, a>0, prove that %3D (i) a = 5 log, (x + y) -q tan log, e- loga (r + y) =…

A: The given isaα+iβ=x+iyp+iq,a>0.prove thati α=12logax+y-qtan-1yxlogaeii logax2+y2=2αp+βqp2+q2

Q: Solve the polynomial congruence x^3 - 3x^2 + 27 = 0 (mod 225). Please be detailed! I’m really…

A: Solution are fully explained in below steps Explanation:

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: If A= xe Z:2" = 1 and B = {x e Z:-4 < 3x-1<11}, then find n(A×B),where Z is a set of integers.

A:

Q: Find all the solutions to the linear congruences  (b) 128x = 833 mod 1001 (c) 36x = 30 mod 42

A:

Q: 5x² + 3x = 3(mod17) X = (mod17)

A: Given that 5x2+3x≡3 (mod 17)x(5x+3)≡3 (mod 17)x≡3 (mod 17)  or   (5x+3)≡3 (mod 17)x≡3 (mod 17)  or…

Q: Solve the congruences: 52x + 4 = 8(mod 22) 17x = 19(mod 100) 3x = 9(mod 12)

A:

Q: 5^14 ( mod 26).

A:

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: Can the sum of divisors of zero be an invertible element?

A: The objective is to state whether the sum of divisors of zero be an invertible element?

Q: 12x = 18 (mod 15) is solvable Select one: True O False

A:

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

A:

Q: Solve the system 3x + 4y = 5 7x + 5y = 6 mod 17 mod 17

A:

Q: how did they get 9x^2 from (x^4)/(5x^2)mod11 ?

A: Use of z11[x],

Q: a) =a +b²

A: Since you have asked multiple questions in a single request we would be answering only the first…

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.