{-74 + 1, ..., 74 – 1}. (b) Hence, find a solution to the congruence x' = 99 mod 74.

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: (a) Solve the linear congruence 26x = 1 modulo 33

A: Solution

Q: Q2: Solve the following (if possible): 1. = 5x + 11 mod 37 3

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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 .

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A:

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

A:

Q: (c) Prove that m is prime if and only if y(m) = m - 1.

A:

Q: (c) Find a value t modulo 7 so that (3+ 7t) does not solve the congruence x® – 1 = 0 (mod 49).

A:

Q: 3/2 (1 +i)"

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

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A: Take k=4 and C=6

Q: Show that the modulus of the quotient of tow complex conjugate numbers is 1, that is :1.

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Q: For which value(s) of k does X₁+kx₂=1 kx₁ + x₂ = 1 have infinitely many solutions?

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Q: (3) Solve for x (give your answer as an integer between 0 and 7: 14 · 51 ≡ x(mod7)

A:

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: 1+3i+2-5i = 10 (1 + i) ¹⁰ = (1 +3i)· (2 - 5i) = +99 + 100i ; 1+2i+3+4i + =

A:

Q: (12) (a) Prove that if x € Z and r² is even, then x is even. (b) State and prove an analogous…

A: We prove following statements by using contrapositive method.

Q: (a) Prove the following: i. 11 + (6 x 4") - 22n = 6 mod 7, 1 is divisible by 131, ii. 8260 iii.…

A:

Q: Find all solutions of the congruence 3 f(x) = 5x³ - 93= 0 (mod 231).

A: The given congruence equation is .We need to find all the solutions of it.

Q: (a) Find an r E Z that makes the following congruence true: 5x = 1 (mod 24). (b) Prove that there is…

A: Solution a: Given  5x≡1 mod 24 For x=1 5≡5 (mod 24) for x=2 10≡10 (mod 24) for x=3 15≡15 (mod 24)…

Q: the congruence + 92 (2), using the method (Bertrand's Postulate). If n > 0 there erists a prime p…

A: Given:- x4-2x3+9x2+4≡0 (mod 72) , using the method (Bertrand's Postulate).  if n>0 there exists a…

Q: Describe geometrically the effect of the transformation T Let A = -(1) Define a transformation T by…

A: We are authorized to answer one question at a time since you have not mentioned which question you…

Q: 1. Show for all natural numbers n that (2k – 1) = 1+3+ ...+ (2n – 1) = n². k=1

A:

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

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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

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Q: Prove that Σ(8i-5)=4n²-n for every positive integer n. i=1

A:

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: Consider the following function. x2 f(x) = x2 - 16 Complete the following table. (Round your answers…

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

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Q: is a1 = 2, a2 =3, and an  = 5an–1 – 4an–2 for n > 2 expressed in explicit formula? true or false?

A:

Q: Prove that Σ₁ iª = n(n+1)(2n +1) (3n² + 3n − 1) i=1 30

A: