If 19 =7 (mod 6) and 27 =3 (mod 6) then 19x 27 = 7+3 (mod 6) 19+27 = 7+3 (mod 6) 19+27 =7x 3 (mod 6) 19+27 =7-3 (mod 6)

Q: 5. 2x 15 (mod 17) 6. 4x 6 (mod 17)

A: According to our guidelines we can do at most three subpart of a question at a time. So please post…

Q: I don't understand why 3n+2 is congruent to 2n+1(modk) and 3 is congruent to 2(modk). Please…

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Q: If x = y (mod n) and u = v (mod n) then which of the following is false. (a) x+ u = y +v (mod n) (b)…

A: Given that x≡ymod n and u≡v mod n. By definition, x≡ymod n implies x-y is divisible by n. Then let,…

Q: QUESTION 4 Which is correct? 24 27 = 5 (mod 4) 72+5=32 (mod 9) 74 = 164 (mod 10) 19 x 27 = 7-3 (mod…

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Q: Prove that if ax = b (modn) then () x = () (mod ()) where d = gcd(a, n). Apply this result to 5x =…

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Q: Is a set {-22,-3,0,1,5,9,10} modulo 7 a RRS? Why? Is a set {-5,-22,-15,-9,-2,5,8,10,25,34,48} modulo…

A: A subset S of the integers is called a reduced residue system modulo n if: gcd(r, n) = 1 for each r…

Q: 3. Find the following: A. 3^0 mod 5 1 B. 3^1 mod 5 3 C. 3^2 mod 5 1 D. 3^3 mod 5 4

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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 integer solutions to the equation 23. + 6x2 + x + 6 =1 mod 74. Explain your method and cite…

A: en x3+6x2+x+6 = 1 mod 71

Q: x = 2 (mod 5) 2r = 22 (mod 8) 3x = 12 (mod 21) (i) How many solutions does it have lying between 0…

A: i)Given thatNotice first that the moduli are pairwise relatively prime, Therefore, we can use the…

Q: Solve : ex+ay =4 (mod 13) E 2 2 (mod 13) Using elimination

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Q: How many codes fit this description?

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Q: Find how many natural numbers n ≤ 1000 are not divisible by any of 2, 3 without repetitions

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Q: True or False: 3^208= 3 mod 53.

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Q: 5. Explain why the congruence r = 2 (mod 4) has no solutions in Z.

A: We have to show that the congruence x2≡2(mod 4) has no solution in ℤ

Q: Find  mod (40, 7) and div (40, 7).   mod(40, 7)=? div(40, 7)=?

A: 1) mod(40,7)  is the remainder when 40 is divided by 7we know that 7×5 =35  and 7×6=42as 7×6=42 is…

Q: 75 (mod 46)

A: Take a number and modulo with 46

Q: What is 2 ^32 mod (5)?

A: mod is the function whose output is always positive. mod is represented by .

Q: System of congruences (smallest +integer for answer): x = 3(mod 7) x = 4(mod 9) x = (1 mod 6)

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Q: Simplify (15-54)(mod 4). (15-54)(mod 4) =(mod 4)

A: Simplify          (15 - 54)(mod 4)

Q: The product of two numbers are 12 and there Least Common Multipleis 6 then Greatest Common Divisor…

A: Given,  Product of two numbers = 12 and Least common Multiple = 6 To find the greatest common…

Q: Question 8 -37 = 3 (mod 5) True False A Moving to another question will save this response.…

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Q: 1) 50 + 90 = + 50: 2) 7 x (25 + 5) = (7 x 25) + (7 x 3) (10 + 15) + 20 = 10 +( 4) (8 x x 9 = x (5 x…

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Q: 5(mod

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