5. Which of the following are inverses of each other? (a)3, 7 w.r.t. mod 20 (b)2, 5 w.r.t. mod 9 (c)4, 7 w.r.t. mod 9 (d)All of these

Q: If m is an integer, and if (m mod 11) = 6, then what is (5m mod 11)? 2 4 11

A:

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: 5. Give examples of the following. Justify your answers.: (c) An integer n such that n is…

A:

Q: If x = y (mod 2) then which of the following is true. i. x and y are both odd ii. either x or y is…

A:

Q: T F 5. To prove the statement: If ab =0 then a = 0 or b = 0, you may assume ab = 0 and a # 0 and…

A:

Q: 4. Find all numbers between -50 and 50 which x mod 13 = 3

A:

Q: .Which of the following integers are the possible one’s digits of a fourth power of any integer? a.…

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

Q: 9. Let a and b be integers. Prove that if a =7 (mod 8) and b = 3 (mod 8), then: (a) a + b = 2 (mod…

A: Your questions solution below in images

Q: 05 If |a+31/2=1 and 2|b+1|=6, then la +b] could equal any of the following EXCEPT * O A.1 B.3 C.5…

A: Topic:- algebra

Q: How do I prove this:  Let d ∈ N and let a, b ∈ Z. Prove or give a counterexample: If a 6≡ 0 (mod d)…

A:

Q: Compute 21200 mod 27.

A: To Find: 21200mod 27

Q: (c) For each integer a, if a 4 (mod 8), then a 2 (mod 8).

A:

Q: 2= 12 mod 2 - - 2 = 11 mod 18 20 = -2 mod 19 - 2= 20 mod 2 - -17 = 20 mod 8 6.7 = -14 mod 11 - -1 =…

A:

Q: The equivalent of Z sub 5 is set of non-negative integers less than 5. What will be the value of 2…

A:

Q: 10. Determine if each of the following propositions is true or false. Justify each conclusion.  (a)…

A:

Q: 1. The value of 419 mod 7 is O 5 0 6 O 3

A: Given that 419 mod 7

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: 16. Which of the following congruencies has NO solution? . A. 24x = 18(mod 39) B. 5x = 4(mod 10) C.…

A:

Q: 1. Which pairs of integers have a GCD of 16 and LCM of 576? a. 32 and 288 b. 48 and 192 c. 80 and 96…

A: 1)  We need to find which pairs of integers have a GCD of 16 and LCM of 576. We know that , the…

Q: He have to Show that lon = (-1)" (mod 1") shall use mathematical moluction Let Pin) := lon a (47"…

A:

Q: III. Fill-in the blanks. Tare more than 1 answer. Choose any. 1. 46 = 26 mod 2. 156 = mod 15 3. 41 =…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Ans Encryt the message GO" by translating the letter, into number, applying the given encrytion…

A: We will use the basic knowledge of number theory and cryptography to answer this question completely…

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: 5. Let n be a positive integer, and assume that a and b are integers such that a = b (mod n). Prove…

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: 4. If x mod 7 = 3, then x27 mod 7 is O 3 0 6 O 5 O 4

A: Given :- x mod 7 = 3

Q: What is the inverse of (show the steps) a) 20 mod 49 b) 7 mod 26

A: Multipart :  We have , 20 mod 49 We need to find Inverse. We know that , if aa¯ ≡ 1 mod m then a¯ is…

Q: How many positive integers n less than or equal to 11,347 satisfy d(n) 1 (mod 2)?

A: We need to find a number of positive integers n≤11347 such that d(n)≡1(mod 2) i.e., , k∈Z.So, we…

Q: 3- Find a positive integer a such that a. a-3(mod 43) b. a 7 (mod 9). c. a-13(mod 23)

A:

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 =…

A:

Q: 7. Let n E Z. Prove that 9n3 6 (mod 27).

A: The objective is to prove the above statement.

Q: (-130 mod 20·265 mod 20) mod 20 ?   clear answer please

A: a mod b gives the remainder when a is divided by b That is we express it as a=b q+ r where r is the…

Q: The inverse of 5 mod 10 а. 5 b. 2 Ос. 10 O d. The inverse does not exist

A:

Q: Need help with a&b

A: For (a), The statement is false. Counter Example: Let x = 2 and y = 3. Notice that xy = 6 ≡ 0 mod 6…

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: Which of the following statements is (are) true? O-23 div 6-4 6 div 23 = 3 6 div 23 = 0 -23 div 6 =…

A:

Q: VI. Determine four values of x that will satisfy the following. 16. x = 4 mod 5 & x = 3 mod 7

A:

Q: T T T F F F 11. 12. 13. If ab = 0 (mod 3), then a = 0 (mod 3) or b = 0 (mod 3). If ab = 0 (mod 6),…

A:

Q: C 1 a b (b²+ c²) mod 2 = ?, a, b, c EN - {0}

A:

Q: I. Determine whether each of these integers are congruent to 3 mod 7. 1. 37 2. -17 3. 86

A: We will find out the required solution.