Which one of the following is correct? a. 30 3 (mod 5) O b. 25 3 (mod 4) Oc. 31 3 (mod 7) O d. 20 3 (mod 6)

Q: Determine whether each of the following statements about fibonacci numbers is true or false a.…

A: The Fibonacci numbers is the sequence of numbers with the common relation between them. A number in…

Q: If today is Thursday, what day of the week will it be 20 days from now? Friday O Monday O Thursday O…

A: Introduction: For two given integers a and n, either n divides a or n doesn't divide a. When, n…

Q: Q If a b (mod n) and gcd (a, n) = d, then gcd (b,n) = d :Select one True False

A: We have check whether the statement, "If a≡bmodn and gcda,n=d then gcdb,n=d" is true are false.…

Q: Let s={xEZ:x+2E6(mod 15)}. Then S is *

A: a countable set

Q: Determine whether each case is true or not : * a. 44 = 13 (mod 3) > b. -55 = 5 (mod 4) → c. 74 = 1…

A: If a and b are integers and n > 0, we write a≡b(mod n) to mean n/(b-a). We read this as “a is…

Q: II. Give FIVE different answers for each of the following. 1. 49 = mod 10 2. 82 = mod 9 3. 100 = mod…

A: 1) Given expression is  49≡______ mod 10

Q: Determine whether each of the following statements about Fibonacci numbers is true or false. a. 2Fn…

A: By definition of Fibonacci series we know that, Fn=Fn-1+Fn-2 , for all n≥2 Also, Fn+1=Fn+Fn-1 , for…

Q: Perform the following calculations. a. (14 + 30) mod 19 b. (14-30) mod 19 C. (3*13) mod 19

A: To perform the given calculations we shall use the following rules…

Q: V. Suppose that a and b are integers, a = 7 (mod 19), and b = 5 (mod 19). Find the integer c with 0…

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Q: Determine whether each of the following statements about Fibonacci numbers is true or false 2Fn >…

A: We have to determine whether 2Fn > Fn+1 For n ≥ 3 is true or false.   Fibonacci Numbers: The…

Q: Prove the assertions below: (a) If a is an odd integer, then a? = 1 (mod 8). (b) For any integer a,…

A: In this question, we have given assertion in terms of congruence modulo here we prove  8(a) if a is…

Q: Which of the following is not correct ? o gcd(e,(p+1) (g –- 1)) = 1 de = 1 (mod (p – 1) (q- 1))…

A: From the given statements

Q: One of the foll owing is not true: Oa 0= 10 mod 5 b None Oc 14=2 mod 6 Od 20 =0 mod 5 Oe -24 mod 6

A: Here we use rules of modular operation.

Q: Which one of the following is correct? a. 30 쓰 3 (mod 5) O b. 25 3 (mod 4) O c. 31 3 (mod 7) Od 20 3…

A:

Q: Which of the following is TRUE? -52%3D0( mod 13) OA. -1=-13( mod 13) OB. 446=-278( mod 7) OC. 1=0 (…

A: Only (A) is true.  The detailed solution is as follows below:

Q: Which is correct? 24 - 27 = 5 (mod 4) 19 × 27 = 7– 3 (1mod 6) %3D 72+5 = 32 (mod 9) 74 = 164 (mod…

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Q: The sum 3(9°+7°) is congruent to: 2 (mod 9.7) None of the choices O This option This option 1 (mod…

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Q: 4. The statement P-> Q is equivalent to -PA Q. 5. To prove the statement: If ab = 0 then a = 0 or b…

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Q: If a = b (mod n) and b =c (mod n) then which of the following is false. a = c (mod n) a = c3(mod n)…

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Q: Disprove the following statements. (a) If n and m are natural numbers, then nm is composite. (b) For…

A: I have given an answer in step 2.

Q: The value of 52003 mod 7 is? 9 O 8 0 3 0 4 0

A: ab(mod c)=d where d is remainder when ab is divided by c.Here a,b and c are integers

Q: Q1 Correct 30.8s Question (334+458) mod 12 (Express your answer as an integer) Christina Agustin's…

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Q: Ti If a = b (mod n) and b =c (mod n) then which of the following is true. (a) a = c (mod n) (b) a2 =…

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Q: B. Prove the assertions below: (a) If a is an odd integer, then a? = 1 (mod 8). (b) For any integer…

A: We will prove the assertions one by one. For the first part we will use the fact any odd integer a…

Q: 25. The value of x in (7x is congruent to 12 mod 17) is O 16 15 9 13 (mod 17)

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Q: Let c, d e Z and m e N. For each statement decide whether it is necessarily true, or whether it can…

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Q: which one of the following is a congruence ? O 39 = 5 mod 5 O 23 = 4 mod 5 O 29 = 5 mod 15 O 48 = 8…

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Q: 2) If a? = b² (mod n), then a = b (mod n) a) True b) False O a) True O b) False

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Q: III. Determine the value of a such that: 10. a = 11 (mod 21) and 90 s a s 110 11. a = 19 (mod 29)…

A: The given questions are related to congruences. The solution is explained below.

Q: I. Find order of 5 mod m, 3 mod m, and 9 mod m J. Find a proper value for d that make the following…

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Q: III. Determine the value of a such that: 7. a = 20 mod 27 and -26 sa s0 8. a = 20 (mod 31) and –15 s…

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

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Q: Which of the following are not equivalent in modulo 7? O 37 O 16 O -5 O 24

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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: If a = b (mod n) and a = c (mod n) then which of the following is true. (a) b = c (mod n) (b) b2 =…

A: We know that the property of congruence

Q: If a = b (mod 5), then... Choose all correct statements. O 2(a – b) = 0 (mod 20) O a³ = b3 (mod 5) O…

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Q: Which of the following is not a possible value for y ≡≡ 17 mod 8 in the equation ? Group of answer…

A: Consider the given equation.

Q: (a) For each integer a, if a? = 1 (mod 10), then a = 1 (mod 10). (b) Let a, b, and c be integers. If…

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Q: If 5x = 12 (mod 41), then the value of x (mod 41) is O 33 O 19 D 27 O 17

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Q: Which of the following is false? a. (x-y+2) = (x-y-11) (mod13) b. (x-y+2) = (x-y-32) (mod 17) c.…

A: Sol:- Check each statement:- a.x-y+2≅x-y-11mod 13Since, 2 mod 13 = -11 , This statement is…

Q: If a = b (mod 5), then... Choose all correct statements. O a3 = b³ (mod 5) O a + b = 0 (mod 10) O a…

A: Option (a), (c), and (d) are correct options.

Q: Let s={xEZ:x+2=7(mod 13)}. Then Sis

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Q: Using Euler's Theorem, simplify the following numbers: p=3, q= 7, x= 3, and a = 1. Which of the…

A: Given :  p=3 ,q=7 ,x=3 and a=1 To find : Using Euler's theorem for solution

Q: 2. Let A = {n? + n € Z :n € Z} and B = {r € Z : r³ – 32³ + 2x = 0 mod 5}. Prove or disprove: A B.…

A: That's easy, just needs a little congruence. Have a great day!!!

Q: Consider the statement P given by: "For all n E Z, if n mod 4 1, then n2 mod 4 = 1." (a) Is P true…

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Q: III. Determine the value of a such that: 7. a = 20 mod 27 and -26saso 8. a = 20 (mod 31) and -15 < a…

A: Please check step 2 for the solution.!

Q: Which of the following congruence is TRUE? a. 2≡5 mod4 b. 76≡31 mod9 c. 1≡1 mod3 d. 18≡3 mod9

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Q: 1 of the above number n, or (65) = Note that the other number is Therefore, we conclude that the…

A: Given that, number is 15  of the given number n

Q: Which of the following are not equivalent in modulo 4? 3. O 5 41 3.

A: 3 ≡ 3 (mod 4)5 = 4.1+1 ≡1 (mod 4)41 = 4.10 +1 ≡1 (mod 4)-3 =4(-1) +1 ≡1 (mod 4)

Q: 4. Determines the result of the following operations: a. (27 – 3) (mod 5) b. (56 – 14) (mod 7) c.…

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