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

Q: Solve the congruence 2x + 3 = 11 (mod 7). (Select all congruence classes below (modulo 7) that…

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Q: Find all solutions of the congruence x2 ≡ 29 (mod 35).

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Q: Find all whole number solutions of the congruence equation.  2x+1≡ 5 mod 4 3x+1≡ 4 mod 9

A: The given problem is to find the whole number solutions for given system of linear congruence…

Q: (Adapted from Richardson problem Solve the congruence 589z = 494 (mod 817). Hint: The solution…

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Q: Find all whole number solutions of the congruence equation.  2x+3 ≡ 8 mod 12

A: # we are entitled to solve one question at a time . Please resubmit the other question if you wish…

Q: Find the smallest positive integer x that solves the congruence: 7x≡5 (mod52)

A: 7x≡5 (mod52)---(1)

Q: he linear congruence 132x ≡ 76 (mod 100) has a solution. Select one: True False

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Q: 1- Determine the number of solutions of the congruence   x4≡ 61 (mod 117). PLZ WITH DETAILS.

A: Given: x4≡61(mod117) 117=32×13 As ϕ(9)4,ϕ(9)=64,6=62=3                  (here 4,6 denotes the g.c.d…

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

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

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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: Take the last four digits ABCD of your student identification number, and let AB and CD be the…

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Q: a) How can an inverse of a modulo m be used to solve the congruence ax ≡ b (mod m) when gcd(a,m) =…

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Q: 7) Solve the system of linear congruences below: x = 2 (mod 7) x = 10 (mod 15) x = 9 (mod 26)

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

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: X=4(mod nod 13) X2-7(mod 15)

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Q: The liñear congruence 9x = 19 (mod27) has 3 incongruent solutions. :Select one True False

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

A: The congruences given are as follows: x3≡11mod 195x≡4mod 19 We are asked to find the value of x that…

Q: 8. Solve the linear congruence, 30k + 14 = 5(mod 11).

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Q: solve the quadratic congruence 7x^2 - 8x +4 = 0 (mod 17)

A: The given problem is to solve the given quadratic congruence equation 7x2-8x+4 = 0(mod 17)

Q: The equation 21x=49 (mod 70) has: 6 non-congruent solutions modulo 70 7 non-congruent solutions…

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Q: 2. Find all solutions of the linear congruence 12x = 9 (mod 15).

A: P

Q: 4. (a) Solve the set of congruences х 1(mod 3), x= 2(mod 4), x = 3(mod 5).

A: We  will solve it by Chinese Remainder Theorem Given  x≡1(mod3)x≡2(mod4)x≡3(mod5) Compare it with…

Q: Solve the congruence: 341x ≡ 2941 (mod 9).

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Q: Find all whole number solutions of the congruence equation. (2x + 1) ≡ 5 mod 4

A: Consider the given congruence equation. (2x + 1) ≡ 5 mod 4

Q: Show that 18! ≡ -1 (mod 437).

A: We have to show that: 18!≡-1mod437

Q: 11. Solve the congruence 4x = 5 (mod 9).

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Q: Solve the congruence: 6x ≡ 4 (mod10)

A: The congruence could be written as,

Q: Determine if x² = 29 mod 541 has a solution.

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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: Find the solutions of the congruence 15z + 19x = 5 (mod 11)

A: This question is related to Number Theory

Q: Find the smallest positive integer satisfying the system of congruences: x ≡ 1 (mod 3) x ≡ 2 (mod…

A: Here we will find out the required value.

Q: 2x ≡ 12 mod 5 5x + 4 ≡ 2 mod 8

A: 1) 2x = 12 mod 5  2x = (5*2 + 2) mod 5  2x = 2  x = 1  (1 is whole number)    Only 1 whole number…

Q: Use Fermat's theorem, show that if ged(a, 155) 1 then a1 = a (mod 15

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Q: Exercise 3. 3x +1= 2 (mod 9) a has no solution modulo 9 b. has six non-congruent solutions modulo 9…

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Q: Find all solutions of the congruence x2 ≡ 16 (mod 105).

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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: Solve the congruence 9x   21 (mod 33).

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Q: Solve the system of congruence's x = 2 (mod 3), x = 4 (mod 5), x = 1 (mod 7)

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Q: Find all the whole number solutions of the congruence equation. 3x 8 ≡ mod 11 3x + 12 ≡ 7 mod 10

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Q: 3. Find all solutions of the congruence: 19x = 7 mod 69 .Show all steps to get full credits.

A: To find the solution of given linear congruence.

Q: Find all whole number solutions of the congruence equation. 2x+3 ≡ 8 mod 12

A: Given that  2x+3 ≡ 8 mod 12  we have to find the value for 'x'

Q: a) Solve the system of congruences: x 3 mod 4 x= 5 mod 7 b) Solve the system of congruences: X 3 mod…

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Q: 3. Find all integer solutions to the pair of congruences (if any) x = 1 (mod 2) x = 2 (mod3) x = 3…

A: To Find: Integer solutions to the pair of congruences(if any) x≡1(mod 2), x≡2(mod 3), x≡3(mod 5)…

Q: The linear congruences x = 3 (mod 6), x = 9 (mod 15) has simultaneous unique solution modulo. .....…

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Q: Find all whole number solutions of the congruence equation. 3x+1≡ 4 mod 9

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Q: 2x = 1(mod 5) 31( mod 7) 5x 9(mod l)

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Q: The linear congruence 8x = 16(mod14) is solvable. False True

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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.