1. Find all x, y, and z such that a) x = 3 (mod 4) x = 5 (mod 21) x = 7 (mod 25) b) 3y = 9 (mod 12) 4y 5 (mod 35) 6y 2 (mod 11) c) z = 1 (mod 12) z = 4 (mod 21) z = 18 (mod 35)

Q: 6 -4 1 8) A =11 -7 2 5 -3 1 6 11 A) A-1 =|-4 -7 -3 3 B) A-1 - 1 1 C) A-1 does not exist. D) A-1. 1 1…

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Q: Why do Christmas and New Year's Day always fall on the same day of the week? O 25 ( mod 7) = 31 (…

A: To explain why Christmas and new year's day always fall on the same day of the week.

Q: 2-) Find all in tegers x such thet 5x = 12 (mod 7) 10x = 4 (mod 1) 7x E 16 (mod 10d ond 1occ < x <…

A: Given: 5x≡12(mod 7) 10x≡4(mod11) 7x≡16(mod 10) and 1000≤x≤3000

Q: Problem MCD = Greatest common divisor (GCD) t them.a, b, c and m €Zsuch that m 22. a-). Prove that a…

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Q: If cy (mod n) andc>0 then a) x= y (mod cn) b) x y (mod n) ) xy d) (mod") None of these

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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: If a cy (mod n) and c> 0 then a) x y (mod en) b) x y (mod n) ) x=y (mod) d) None of these :Select…

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Q: л There

A: We prove our result by using definition of mod.

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

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Q: 1. How many solutions( mod 419) does x = 186 mod 419 have? (Show your work!) 2. How many solutions (…

A: Given: x2≡186 mod 101  To find: Number of solutions that exists. Method Used:  For any, xk≡b mod p,…

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

A: Given that x≡y (mod n) and u≡v (mod n)

Q: 3. Solve the system of congruences x = 1(mod 5) x 2(mod 6) r= 3(mod 7)

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Q: 1. A+B (mod 173) 2. C-D (mod 432) 3. 23 x E (mod F) 4. G+5 (mod 7) АВМ 1А A B C E F G Hannah 7550…

A:

Q: Suppose that a and b are integers. a ≡ 7 (mod 13) and b ≡ 9 (mod 13). Find the integer c such that 0…

A: The given problem is to find the modular values of c for the given conditions with given integers a…

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: 11. Solve the systems of congruences: a. x = 7(mod 11), x = 4(mod 24) b. 3x = 11(mod 17), 2x = 3(mod…

A: The given problem is to solve the given system of congruence equations. Given system of congruence…

Q: 4. Using your work from the earlier parts or independently find: (a) mod 8 (b) + mod 23 17 (c) mod 7

A: Given

Q: If a≡3 (mod 11) and b≡9 (mod 11): (a) Compute a+b(mod 11) (b) Compute a^3(mod 11)

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Q: III) Are there positive integers x and y suct that x³ = 2² +15? (Hint: for every integer x, x³ 0, 1,…

A: We shall show that no such positive integers exist.

Q: IfOcy (mod n) and e> 0 then a) *= y (mod cn) b) x= y (mod n) ) x=y (mod) d) None of these :Select…

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Q: The solution of the linear congruence 4x = 5(mod 9) is? 6(mod 9) 10(mod 9) Qmod 9) 8(mod 9)

A: Since, x = 9 n + 8 and n element Z Now,  4x congruent 5 mod 9 implies  x congruent 8 (mod 9).

Q: I have a message 2,3,6,5 (mod.7),  I will find a check digit by multiplying the first and third…

A: Here, First number= 2 Second number =3 Third number= 6 Fourth number= 5

Q: 1. What is the remainder when 65544 - 13 is divided by 8?

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Q: 9. Prove that if n = 3 (mod 4), then the equation x² + y² = n has no integer solution.

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Q: Evaluate the following: 495 (mod 11) 3(mod 8) 2345(mod 6) (i) (ii) (iii) 9

A: As per bartleby guidelines we only give first three questions answers. Please repost for other…

Q: 11) The solution of the linear congruences x = 1 (mod 2), x = 2 (mod 3), x = 3 (mod 5), x = 4 (mod…

A: We have to find value of x

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: Suppose that a = 3 mod 12 and b =7 mod 12 IfC = 3 a – 2 b mod 12 then C =

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Q: 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)…

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Q: (6) The addition property of modular arithmetic can be written as: (Choose one answer from below) A)…

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Q: If a = b (mod n) and b = c (mod n) then which of the following is true. (a) a = c (mod n) (b) a? =…

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Q: Let n1, n2, n3 be three numbers that are pairwise relatively prime so that (n1, n2) = (n2, n3) =…

A: Given that n1,n2 and n3 are three numbers that are pairwise relatively prime. We have to prove…

Q: 5) Which are true and which are false? a) 3XER,x^2-4x+5=0 b) VxɛZ,x^2 =0(mod4)orx^2 =1(mod4) c) Vx E…

A: In the given question we have to tell about some given statement which of them are true or which of…

Q: 2 (-3) - = (- (-1)² 8 = {) 1 -1 if p= ±1 (mod 8) if p= ±3 (mod 8).

A:

Q: Ksi7 is not Show that ksit regular. is not

A: We can solve this using regular graph definition

Q: 13. Suppose that a and b are integers, a = 4 (mod 13), and b = 9 (mod 13). Find the integer c with 0…

A: Since you have posted a multi subparts question according to guildlines I will solve first…