Q3/ Use Chinese theorem to solve the following congruence: X=2 mod 3 X=1 mod 5 X 2 mod 4

Q: What is the number of solutions to the congruence in Z125? x³ + x² + 3 = 0 (mod 125)

A: As per the question we have to solve the following polynomial congruence equation : x3 + x2 + 3 ≡ 0…

Q: Prove that x113+x-1≡0(mod 113) has no solutions in x.

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Q: ​Q3// Use Chinese theorem to solve the following congruence: X ≡ 2 mod 3 X ≡ 1 mod 5 X ≡ 2 mod 4

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

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Q: (10) Find all solutions of the congruence 2 = 22 (mod 53). C

A: We shall be using primitive roots to solve this congruence.

Q: Q16

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Q: 1. Find all solutions (a) 2x + 3 = 7 (b) 2x + 3 = 7 to the following congruences.. (mod 9) (mod 20)

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Q: Solve linear congruence 45x ≡ 60 (mod 75)

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Q: solve the congruence 2²-7x+6=0(mod3³.7³)

A: Given congruence: Objective: Solve the congruence equation and find the solutions for  modulo .

Q: Solve the con Congruence 1x²=6 (mod17)

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Q: Determine the truth value of the statement and prove it on a sheet of paper: D = set of integers vn…

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Q: Solve the linear congruence 2370x ≡ 69 (mod 2517) or say why no solutions exist

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

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Q: Find all solutions of each congruence and explain why these are all the solutions. (It is possible…

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Q: The quotient of 33288

A: Given: 33288

Q: x43 = 47 (mod 713)

A: Step:-1 By Chinese remainder Theorem (CRT),  x43 ≡ 47 mod 713 if and only if x43 ≡47 mod 23 ⇒x43 ≡1…

Q: Solve the system of congruences 2x ≡ 1 (mod 5) 3x ≡ 9 (mod 6) 4x ≡ 1 (mod 7) 5x ≡ 9 (mod 11) Hint:…

A: We can solve this system of congruences using the Chinese Remainder Theorem. First, let's write each…

Q: Solve the congruence 11x = 45 (mod 97) where x is an integer in the interval [0,97).

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Q: 1. Solve the Congruence x^5 ≡ 2 (mod 7)   2. Solve the congruence x^7 ≡ 10 (mod 23)   Show work…

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Q: Solve the givnen congruence x2 ≡ 9 (mod 600).

A: The given problem is to solve the given congruence equation. x2=9 (mod 600).

Q: 2. Encrypt the message STOP POLLUTION by translat- ing the letters into numbers, applying the given…

A: let's encrypt the message "STOP POLLUTION" using the given encryption functions one by one.For the…

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: Solve the congruence3x−7 = 2 (mod 16). Your solution should be positive and reduced modulo16.

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Q: for a fixed n>1 Show that all the solvable congruences x2 ≡ a ( mod n ) have the same number of…

A: To Proof: For a fixed n>1 , all the solvable congruences x2 ≡ a ( mod n ) have the same number of…

Q: solve the congruence of  6x=4 mod 10  aolve the conguence of 341x=2941 mod 9

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Q: . Find all the solutions of 3x² + 2x + 1 8 (mod 63).

A: Given a quadratic congruence in the form:Ax2+Bx+C=0(mod n)multiply the above equation by…

Q: Consider the congruence 9x   21 (mod 33). (a) Does 9 -1(mod 33) exist? Explain why or why not.

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Q: X = 17 (mod 21) X= - ) 8 Cmod 25

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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: 1 Solve the following system of congruences X= 2 (mod 3) x = 3 (mod 5) X= 2 (mod 7)

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Q: Demonstrate that the equation x10 + y10 - z10 = 5 has no integer solution. (work with modulo 11)

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

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Q: Chosse the correct answer. A particular solution of x'' + x' - 2x = 2sin2t is given by: Xp(t) =…

A: Given non-homogeneous differential equation x''+x'-2x=2sin2t    ...(1). We have to find the…

Q: Solve by using the Chinese remainder theorem for the congruence X 2 (mod 7) X 4 (mod 5)

A: Given that This can be written as,

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

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Q: Find all solutions of the systems of congruences: = 12 (mod 25) 22 (mod 35).

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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)

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Q: If possible, find a complete set of mutually incongruent solutions of each of the following…

A: The given congruences, a) 9x≡12mod 15. b) 81x≡57mod 117. We have to find the solution to the…

Q: B. Using Fermat's Theorem •Determine all solutions of the equation 6x = 18 in Z24. •Describe all…

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Q: congruences using the modular inverses found in question 11. 4 (mod 141) 34 (mod 89) Solve the…

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Q: Solve the linear congruence 7а + 3у %3D 10 (тod16).

A: Consider the linear congruence 7x + 3y ≡ 10 mod 16.Since gcd (7, 3) = 1 we know at least one…

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.