11. Define conguren ce class es for modulo 4.

Q: U(12) under multipilcation modulo 12

A: To find U(12) under multiplication modulo 12.

Q: 2show that O (ir Yational numbers iihot hegigitale

A:

Q: If a = b (mod m) and a = b (mod n) then a = b (mod mn)

A:

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

A:

Q: What is the remainder when 2021202120212021 is divided by 2020? use congruence modulo

A: a = 2021202120212021 b = 2020 If a = qb + r then  a ≡ r mod n.

Q: Suppose that 54% of people own dogs. If you pick two people at random, what is the that they both…

A: Given: P(Dog) = 0.54 The probability that they both own a dog can be calculated as: P(Both own a…

Q: 1. Show that subtraction is not associative for the set of integers.

A: Definition :Let "." be a binary operation and A is a setThen "." is said to be associative for A if…

Q: Name all integers from -100 to 100 that are congruent to -1 modulo 25!

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Q: The set {1,2,3,4} under multiplication modulo 5.

A:

Q: Suppose that 43% of people own dogs. If you pick two people at random, what is the both own a dog?…

A: Given, Probabily of a person own a dog is 43 %

Q: Compute the addition modulo operation 3+2 2 0. 1 3 O O

A:

Q: from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 form a set containing first five prime numbers (x) greater than 50…

A:

Q: The inverse of 7 modulo 26 is 15

A: Given a statement

Q: Prove: in L number psiz 12, for every prime poiz, [p] = [1], [5) , [7) , or [11]

A:

Q: 3. Show that ifn = 2 (mod 4), then 9" + 8" is divisible by 5.

A: Here we will prove the given statement.

Q: What is the least residue of 7162 modulo 17?

A: Multiplication rule for congruencesIf a ≡ b (mod n) and c ≡ d (mod n), thenac ≡ bd (mod n). Power…

Q: The set {0,5,6} is closed under Mod(10)

A: To check if { 0 5, 6} is closed under mod(10)

Q: Prove Simple disprove is Bing That Characteristic af Prime or either Zero or

A: A simple ring R is a ring with unit such that the only two-sided ideals are R and (0). The…

Q: modulo 5   B).  Evaluate 31mod5

A:

Q: How many integers have inverses modulo 144? Justify.

A: Justify how many integers have inverse modulo 144.

Q: 1. How many positive integers of 5-digit-number can be formed from the prime numbers starting at 1…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 2. In Section 3.1, we defined congruence modulon where n is a natural number. If a and b are…

A:

Q: The prime number 8191 is a None Mersenne prime number Carmichael number Inverse of 7 modulo 11

A: Given that The prime number 8191 is

Q: 6. The set A = (0,1,2,3} under multiplication modulo 4

A:

Q: Is it true that 90 ≡ 64 (mod 13)?

A: As given equation 90≅64(mod 13) is False.

Q: List six intergers that are congruent to 7 modulo 9.

A:

Q: Let n, m, a, b be positive integers. motl Lof oontredietion u th

A: Given, n, m, a, b be positive integers. To prove that…

Q: 7. Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?

A:

Q: 2. Create the following tables: (a) Addition table for modulo 7 (b) Multiplication table for modulo…

A:

Q: 122 is congruent to 5 modulo17 ?

A: To check whether -122 is congruent to 5 modulo 17 or not

Q: Is 17 congruent to 4 modulo 6.

A: 17, when divided by 6, leaves remainder 5

Q: Motorcycle license plates in the state of California start with two digits(0–9), followed by one…

A: There are a total of 6 digits and one letter on the license plate and repetition is not allowed.…

Q: Find oll integers Such thot 24! x =1 Cmod 2) 5x = 3. (mod 8) and 1500 < X <2000

A:

Q: To Determine the value that 46 is congruent to IN modulo 7

A: Note that, If a and b are integers and n &gt; 0, then a ≡ b (mod n) to mean n|(b − a) and It can be…

Q: In the set {0,1,2,3,4,5}, this is the additive inverse of 4 under addition modulo 6. What is the…

A:

Q: Prove that a four-digit number is a multiple of 8 whenever the number formed by the first three…

A: The solution is given by using the expanded form of number as follows

Q: Suppose that there are 27 students in discrete mathematics class. Show that the class must have at…

A: Here we solve this question by contradiction.

Q: If 3x = 6 mod 9, when -2 <x< 8. Then O x=(-1, 3, 5} x=(-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

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Q: Inverse of 9 modulo 23 is 18

A:

Q: 29 is a primitive root modulo 38? True or False

A: The answer to this question is TRUE.

Q: A1. How many integers, greater than or equal to10000 but less than or equal to 39999, can be formed…

A: Since you've asked multiple parts questions, as per our answering guidelines we are supposed to…

Q: If 3x = 6 mod 9, when -2 < x< 8. Then O x={-1, 3, 5} x-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

A:

Q: 1. Show that 1105 is a Carmichael number.

A:

Q: Prove that every third Fibonacci number in 0, 1, 1, 2, 3, ... is even.

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Q: Show that : If n is an integer then n is congruent to 0 modulo 4 or 1 modulo 4.

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Q: Prove that no integer congruent to 3 modulo 4 can be written as the sum of two squares.

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Q: Determine whether 17 is congruent to 5 modulo 6?

A: We have to check whether 17 is congruent to 5 modulo 6

Q: Two integers are congruent modulo to a)prime integer b)odd integer C) not a prime nor composite…

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Q: Find the order of 5 modulo 31.

A: