Problem MCD = Greatest common divisor (GCD) t them.a, b, c and m €Zsuch that m 22. a-). Prove that a = b (mod m), then MCD(a, m) = MC D(b, m). b-1 Show that ac = bc (mod m), then a= b (mod m MCD(c,m)

Q: 5. Verify if the following are difference sets and state v, b, k, r, A for the ones that are: a)…

A: 5(a) Given that, (0,8,15,17,20,21)mod31 The cardinality of the set is 6 with mod31. Here V is the…

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: Let a, m € Z+ and (a,m) = (a - 1, m) = 1. Then prove that 1+a+...+ a(m)-1 = 0(modm)

A: For given,       (a,m) = (a -1, m) = 1 We have to show,      1 + a + a 2 + ........ + a φ (m)-1 ≡ 0…

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: For each statement, indicate whether it is true or false. Then prove or disprove it. (a) For all SC…

A: (a) FALSE.  Consider S ⊆ℤ, defined by  S = { 2+8k | k ∈ℤ } U { 2+12r | r∈ℤ }.  Then the given…

Q: Show that (p-1)(p2) (pr) (-1)'r!(mod p), for r= 1, 2, . . . ,p - 1. .

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Q: If al = b (mod p), then prove that a = b (mod p).

A: (ii) given that                                                ap≡bp   (mod p) we have to prove…

Q: 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)…

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Q: 15 Composite Then and O modn Show that if n there are with X#0 od n and y7 but where yy= Omod n.

A: Given n is a composite number

Q: Prove that's is prime p, then (a + b)² = (a² + b²)(mod p), Va; b € Z

A:

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: 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: 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: 2. Prove that if a = b( mod r) and c = d( mod r) then a – c= b – d( mod r)

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Q: Fin o all SoinEl ons 6 x EIO mod

A: For x in {0, 1, 2, . . . . . 43}, value of 6x ranges from 0 to 6x43 = 258. Now 6x = 10 (mod 44)…

Q: For the following linear programming problem, determine the optimal solution by the graphical…

A: Given that                                        Objective function, z=-x+2yconstraints,…

Q: *1. What is the least residue of 56 (mod 7) 58 (mod 7) 19458 (mod 7)?

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Find the first few terms of the sequence of pseudorandom numbers generated using the linear…

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Q: Find the first few terms of the sequence of pseudorandom numbers generated using the linear…

A:

Q: 16. Prove that an integer (a,-1an-2 · . . ao)10 is divisible by 11 if and only if ao + a2 + a4 + . .…

A:

Q: (a) Show that a solution to the equation above is u(t)= xet, where x and A are an eigenvector and…

A: A=3-221 Finding the characteristic equation of the matrix ∴A-λI=0⇒λ2-4λ+7⇒λ=4±16-282       =2±i3 The…

Q: If a =b (mod m) then a" = b" (modm) Vn e Z*.

A: Given a≡bmod m. we have to show that an≡bnmod m. we wil prove this by result by using method of…

Q: 13. Suppose that z1 V3 +i and z2 = 2/2+ 2v2i. 22 (a) Write z1 and z2 in mod-arg form. (b) Hence…

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Q: 2. Find the largest negative x € Z that simultancously satisfies 4x = 9 (mod 5) 2x = 0 (mod 6) x =0…

A: Given : 4x = 9 (mod 5) 2x = 0 (mod 6) x = 0 (mod 4)

Q: 20.What is the value of n such that (24  is congruent to 58 mod n) ? a.13 b.17 c.-34 d.-13

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

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: Need help with True or False for the following... (I will put what I believe As (T) or (F)) 1. For…

A: Let's evaluate the provided statements and their negations as well as the converses and…

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. Verify if the following are difference sets and state v,b, k, r, A for the ones that are: a)…

A: Given different sets, state v,b,k,r,λ .

Q: Work the modular arithmetic problem. (12 9)(mod 3). (12 9)(mod 3) =(mod 3)

A: The given modular arithmetic problem is -  (12·9)(mod 3) We have to solve the above problem.

Q: If nez then I89?bmodm a=+b moad m

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Q: 4. A linear code is given by the encoding function y = ax+b (mod 26) and the decoding function x =…

A: 4.(a) Given a = 11, b = 2, the encoding function is given by         y ≡ 11x + 2 (mod 26)…