1+n 3n+1 For each natural number n, Let - Find UA, and 4. n n EN EN If R={(x, y) & RxR: x² = 3 +5y}, S={(x,y) & R×R: y³ = 3x²+5}, Then find RoS and SoR Solve the simultaneous congruences: x = 3 (mod 2) x = 5 (mod 7) (x = 11 (mod 13)

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: Solve the following congruences: (a) 3x  8 (mod 5) (b) 3x  8 (mod 12)

A:

Q: (1) Determine the number Sm of solutions to the equation xyz = 1 (mod m) for each positive integer…

A: Given that:To find:The number  of solutions to the given equation for each positive integer…

Q: Q16

A:

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

A:

Q: (3). (a). Find all solutions to the congruence 6x = 9 (mod 45)

A: To Determine :-  All solutions to the congruence : 6x ≡ 9   mod 45 .

Q: 2. Solve for X, show all calculation in binary number system only ((11111000)2 X = ((1101), –…

A: First, solve the first bracket 1101 - 0010 = 1011 which is in decimal equivalent to 13-2 =11 then…

Q: Find all solutions to the system of congruences: x ≡ 7 mod 12 x ≡ 37 mod 45 2x ≡ 134 mod 150

A: The given problem is to find the all solutions which satisfies the given system of linear…

Q: Show that x2 = Y mod p has

A:

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

A: Given:- 15x2+19x≡5 mod 55

Q: Find all solutions of the system. 3x = 1 (mod 5) 2x = 3 (mod 7) 5x=11 (mod 3)

A:

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

A:

Q: Solve the congruence17x−3 = 4 (mod 26).

A:

Q: The least positive integer solution for the congruence 2x = 14 (mod 18) is Answer:

A:

Q: Can you please show me step by step for this math that makes me undertandable. Q: Determine which…

A: (a) For the congruence 4x ≡ 5 (mod 6), we need to find a solution for x such that when 4x is…

Q: The modulus of 5 + 4i is * -41 -√41 √41 41 The conjugate of (i-i² )³ is -2-2i O 2+2i -2+2i Oi-1

A:

Q: 1) Find a solution – if possible – for each of the following two congruences. If for one of the…

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: B- State Fermat little theorem, then find √√27 mod 31. Find (52525).

A:

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: 2x = 4 (mod 8) a. has no solution b. has infinite solutions c. has a unique solution modulo 8 which…

A: Here 2x≡4 (mod 8). Hence 2x=4+8k, for some integer k. Dividing by 2, x=2+4k, for some integer k.…

Q: 16y = 18 (mod 12) is solvable Select one: True False

A: Solvable means,there exist an integer for which equation satisfies,  not solvable means there is no…

Q: (2) (a) Find all of the solutions modulo 15 to 6x = 15 mod 18. Express your answer in terms of the…

A: Given, 6x≡15 mod 18. As it is known that, an≡bn mod cn ⇔ a≡b mod c. Therefore, we have 6x≡15 mod 18…

Q: Find the solutions of the congruence 15x2 + 19x ≡ 5 (mod 65)

A: The given equation is: 15x2+19x≡5(mod 65)

Q: Solve the system of congruence x ≡ 3(mod6) and x ≡ 4(mod7) using the method of back substitution.

A: System of congruence equations

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

A:

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: Find all the solutions of 15z = 27 (mod 18).

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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: (a) Let p E N be a prime number, p # 5, and let nE N. Determine the number of solutions to the…

A: First note that this question is only solvable for certain primes and not for all primes. We…

Q: k from problem 2 and the method used in the example at the end of solve the congruence: 7x³ = 6…

A: Given: Congruence is To Find : Solve the congruence equation

Q: How do I use the Chinese Remainder Thm to solve this system of congrunces below? x ≡ 1 (mod 3) x ≡ 4…

A:

Q: . (a) How many quadratic residues are in the residue set Z19? (b) Determine if 4 and 9 are quadratic…

A: Introduction: Quadratic residue is related to congruent modulo theory. Since, it deals with…

Q: Use the index system modulo 19 to find all solutions of x³ = 11 (mod 19) and 5ª = 4 (mod 19)

A: In the theory of congruence, Fermat's little theorem is very significant. It says that for any prime…

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

A:

Q: 2x² + 3x = 14(mod19) X = * (mod19)

A: Given,            2x2+3x≡14 (mod 19).

Q: olve the congruence8x= 16 (mod 424).  If none exists, explain why.  If there are one or…

A: The given equation is: 8x≡16mod 424