Furthermore, any two solutions x and y are congruent modulo n¡n2 · Solve the following systems of congruences. b. x = 4 (mod 5) x = 2 (mod 3)

Q: 8.) What is the distance between an airplane flying at 120 feet above sea level and a turtle…

A: We find the distance between an airplane flying at 120 feet above sea level and a turtle swimming at…

Q: A. 5x = -127 mod 15.

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

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

A:

Q: True or False. Provide justification. The system x ≡ 3 mod 18 and x ≡ 7 mod 20 has a unique solution…

A: We see, possible solutions to x ≡ 7 mod 20 modulo 180 are     x ≡ 7, 27, 47, 67, 87, 107, 127, 147,…

Q: Solve a congruence equation and give all the solutions: 3(x – 2) + 4x = 5x +8 (mod 31)

A:

Q: Find the common solutions to the congruences 2x 3x 4x 1 (mod 5) 9 (mod 6) 1 (mod 7).

A: Given : 2x≡1 (mod 5)3x≡9 (mod 6)4x≡1 (mod 7) To find : The common solutions to the congruences. For…

Q: 1. For each solution: determine weather there is a a congruence a x² = -1 (mod 397) b.) x²+8x+14=0…

A: 1a) To determine whether the congruence equation x2 ≡ -1 (mod 397) has a solution, we need to check…

Q: Q7. Solve the following set of simultaneous congruences. 4x = 1(mod 5) 6x = 5(mod 11) 2x = 5(mod 13)

A:

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

A: Topic:- algebra

Q: Find the solutions of a3 – 24.x2 + 54 = 0( mod 25).

A: want to find solution of x3-24x2+54≡0(mod 25)note that1 a≡b(mod m) f and only if m|a-b(i.e a-b=mk…

Q: Find all solutions for x, up to congruence. (b) x ≡ 11 mod 142 and x ≡ 25 mod 86.

A: Given: (b) x≡11 mod 142 and x≡25 mod 86 To find: All solutions for x, up to convergence.

Q: (3) If today is Thursday what day of the week will it be 31 days from today? (4) If it is currently…

A:

Q: 11. Solve the systems of congruences: a. x = 7(mod 11), x = 4(mod 24) b. 3x = 11(mod 17), 2x = 3(mod…

A: The given problem is to solve the given system of congruence equations. Given system of congruence…

Q: D. Determine the number of incongruent solutions of each linear congruence. 1. 22x = 18 (mod 75)…

A: Given linear congruence is  1. 22x≡18mod 752.   2z≡119mod 983.   9x≡95mod 36

Q: 1. Solve each of the linear congruence equations or verify that it has no solution. (i). 3r = 4(mod…

A:

Q: Exercise 34 Solve the following equations: 1. 5x +3 = 7 (mod 11). 2. 4x + 5 = 11 (mod 13). 3. 9x – 4…

A: As per our guidelines we are supposed to answer?️ only 3 subpart from multiple questions. Kindly…

Q: Solve the following linear congruences (you may if you wish, find some solutions by inspection): (a)…

A:

Q: x = 10 (mod 18), x = 14 (mod w). Solve system of congruences, find the smallest possible value for…

A: given x≡7mod 15   ...ix≡10mod 18   ...iix≡14mod ω   ...iii where ω≥20 to find solve system of…

Q: Solve each equation for x. (If there is no solution, enter NO SOLUTION.) (a)     x + 8 ≡ 1, (mod 9)…

A: We solve each equation for x.

Q: If possible, solve the following linear congruences. (a) 42x = 1014 (mod 91) (b) 42x = 1015 (mod 91)

A: If possible, we have to solve the following linear congruences.

Q: y²=x³-5x+3 (mod5). solve for all x and y, when x is at least 0, and y is at most 4

A: Using congruence and modular arithmetic we solve the given equation. We substitute the value of x…

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

A:

Q: Explain why the following linear congruence has no solutions:   5x ≡ 16 (mod 45).

A: Explain why the following linear congruence has no solutions: 5x ≡ 16 (mod 45).

Q: 5. Solve the following quadratic congruence using the "completing the square" method: 9x² +66x +49 =…

A: 5. Given equation is 9x2+66x+49≡0(mod 79)   To Solve: Above quadratic congruence using the…

Q: The equation 15x=30 (mod 50) has: 5 non-congruent solutions modulo 50 6 non-congruent solutions…

A:

Q: Determine whether the following systems have unique solution, infinitely many solutions or no…

A:

Q: Solve the quadratic congruence x² = 35 (mod 817).

A:

Q: Q7. Solve the following set of simultaneous congruences. 6x = 1(mod 5) 5x = 3(mod 11) 2x = 5(mod 13)

A:

Q: 2X−4Y+6Z≡3 (mod8)  2X−4Y+6Z≡3 (mod8) 3X+6Y−9Z≡1 (mod19) 3X+6Y−9Z≡1 (mod19)

A: This is a problem of modular arithmetic, number theory.

Q: 96. Solve the congruence 13 – 29x2 + 35x + 38 = 0 (mod 195).

A:

Q: -) Find the solutions, if any, of each congruence. 21x 10 (mod 35) 9x = 15 (mod 21).

A: We know that, ax≡b mod n has solution if and only if gcd(a,n) divides b.

Q: 2) Solve the following linear congruences: 14x = 91 (mod 189) 24x = 56 (mod 88)

A:

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

A: As per our guidelines we supposed to solve the very first question when multiple questions are…

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

A:

Q: The number of mutually incongruent solution(s) of 306x = 90 (mod 360) 20 30 18 O 60

A:

Q: Please try to explain how did you solve it Q: Solve the following congruence 5x+8 ≡ 11 (mod 22).…

A: We are given the congruence relation          5x + 8 ≡ 11 (mod 22)        => 5x ≡ 11 - 8 (mod 22)…

Q: he solutions of the equation 7? ≡ 28 (mod 119).

A: We have to find out all the solutions of the equation 7?≡28(mod 119) ax≡b(mod n) has solution iff…

Q: The number of mutually incongruent solution(s) of 306x = 90 (mod 360) 20 30 18 O 6 0

A: