3. First solve for q: (a) 143 = 1( mod 2) (b) Rewrite 143 as the product of 11 x 13 and show that (11( mod 2))(13( mod 2)) will give you the same remainder of 1.

Q: Show that 4x2+6x+3 is a unit in Z8[x]. All that I know that I have to do is find a polynomial such…

A: Given polynomial is,

Q: 2. Find the root using Regula-Falsi Method a) x* - x - 10 = 0 Ans. x = -1.697 and 1.855

A: Follow the procedure given below.

Q: the fourth power of an integer is x, and x is between 100 and 600. What is x?

A: It is given that the fourth power of an integer is x.That is, x = n^4, where n is a positive…

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

A: Given:- 15x2+19x≡5 mod 55

Q: 7. Suppose a1, a2,...,ɑn are integers, r is a solution to the equation 1" + a,r"-1 + a2r"-² + + a, =…

A:

Q: Find the smallest integer value c and it's n, to show that 2n2 + 6n – 3 Oln –10) is an

A: Given:

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: 32+104 ≡ x(mod5) How do you solve these?

A:

Q: B. Solve for the indicated term of each expansion. 1. The 7" term of (xi -- 10

A:

Q: , 7/4 /213, 33 b) Solve e In(9) + 21 = 41 for æ. a) Write In(- -) in the form a lIn(7) + bln(3)…

A:

Q: 3x = 11 (mod 20)

A:

Q: 1.Solve the following integer LP using branch and bound method: + 5 x2 MAX Z= subject to: + 10 < 20…

A: Answer

Q: Prove that the last two digits of 2" cannot be 02 and the last three digits cannot be 108. Find all…

A: All these problems can be solved using modular arithmetic. We presented the detailed solution in the…

Q: (b) Since 61 is a prime with 61 = 1 (mod 12) the polynomial X? + 3 has roots in Z/61Z by (a): they…

A: Here we need to solving ....(i) knowing that .....(ii)

Q: Find a simple closed expression for computing E=1k²Hx and verify your answer for n = 4.

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Solve the equation modulo 5.  2x+3=1

A:

Q: (d) 9r = 3 (mod 5) (e) 5x = 1 (mod 6) (f) 3x = 1 (mod 6)

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: By using the iterative formula Xn+1 and xo = O O 0.3652 O 1.3652 O2.6352 = 1.5, then the value of x5…

A: Find the value

Q: B. Find the coefficients specified in each item. 2. a² in (6 - 1/2a)6 a4 4. k4 in (3k – 21)¹2

A:

Q: (i) Deduce that the difference in the number of integers in the numerator and denominator of (* 2N N…

A: Properties of floor functions will be used.

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: Solve for x: 32 +104 = x(mod5) O 3 O 2 4. 1,

A:

Q: Find all the solutions r E Ziz to the equation r³ – 5x² – 7x = 0 mod 13.

A: First, solve in real number then ring down to the finite field.

Q: 2X+3=1 mod 5 Show your work

A: We have solve given problem:

Q: Proceed as in Example 3 in Section 6.1 to rewrite the given expression using a single power n(n –…

A:

Q: 37! D- Given that N= (191)(15) is an integer: i- Does the prime 11 divide N? What about the prime…

A: N = 37!19! 15!37! consist numbers that are divided by 11→11, 22 , 33→319! consist numbers that are…

Q: 10 Solve 3Y=2 (mod 7) 8 Salutions exist or show that

A: We have to solve given problem:

Q: Q4 (a) Solve for x if 25x = 15(mod 29). (b) Determine the smallest positive integer so that when…

A:

Q: 10. Solve the following quadratic equation via the two different methods namely both classical and…

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: 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: 8. Solve the following quadratic equation via the two different methods, namely both classical and…

A:

Q: Solve for x using a =b mod m) iff mlla-b): 8 I lx-19)

A:

Q: (12) What values can be assigned to r so that {4n+r} will include all odd primes?

A:

Q: b. 3x = 0 (mod 21)

A:

Q: 6. Find the root using Regula-Falsi Method a) x* -x- 10 = 0 Ans. x = -1.697 and 1.855

A: As per our company guidelines, we can solve first question for you. If you want other question to be…

Q: 5. (8x*y® + 3x³) dx + (12x°y³ + 3xy²) dy = 0

A:

Q: 9. a. Solve xQ + Q – 4 = 3Q + 5 (mod 2Q), where Q = 2 b. Find the quotient and remainder when Q is…

A: 9. a) Given congruence is xQ+Q-4≡3Q+5mod 2Q where Q=2 Using the value Q=2 in the given congruence…

Q: 3.2.6 Find all solutions x to the congruence equation 12x = 1 (mod 17)

A: Given, 12x = 1 (mod 17) So, 7•12x = 7•1 (mod 17) So, 84x = 7 (mod 17)

Q: Compute the exact answer mentally by finding compatible numbers or substitutions: 4x 273 x 25 4x273…

A: The steps are as follows

Q: b. Find r with 0 <r< 601 such that 257 = r mod 601. c. Find the last two digits of 3140 (when…

A:

Q: Solve x 3D 1(mтod4) x = 3(mod6)

A:

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

A: Use of z11[x],

Q: 6. Find a prime number p for which the equation x² = -1 mod p has no solution.

A: Given is a  modular equation.   To Find: A prime number p such that the given equation has no…

Q: 10. Solve the following quadratic equation via the two different methods namely both classical and…

A:

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.