Calculate the least residues modulo 5 of 14, 24, 34, and 44.

Q: Write a complete residue system modulo 13 consisting only of odd integers.

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Q: 3. Find the number of distinct permutations that can be formed your ID number.

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Q: Least residue of 8^68 modulo 17

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Q: If positive integers are chosen at random, what is the minimum number you must have in order to…

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Q: A phone number is a 7-digit that does not start with 0. Call a phone numbers that make up of exactly…

A: According to the permutation rule, if r distinct items are to be chosen from n items without…

Q: list five different natural numbers that are congruent to 10 modulo 4

A: We know that a≡b(mod m) if m  divides a-b 14≡10 (mod 4)  ∵ 14-10 =4 which divides 4 18≡10 (mod 4)  ∵…

Q: Find the least residue of 63^9 modulo 10

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Q: from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 form a set containing the first four fibonacci numbers (x) that…

A: given the set

Q: Compute the 3^201 mod 5.

A: Congruence value

Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?.

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Q: How many bit strings contain exactly eight Os and 10 Is if every 0 must be immediately followed by a…

A: Solution

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

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Q: Assume n and m are two integers such that n > m > 1. If a bit string of length n+m is randomly…

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Q: Find the least residue of 448 modulo 7

A: Given problem is : Find the least residue of 448 modulo 7

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: Find the least residue of  -5 -46 modulo 14.

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

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

Q: Number theory

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Q: Find the sequence of pseudorandom numbers generated by the power generator with p = 7, d = 3, and…

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Q: Find the least positive integer n that satisfies the congruence 7 ^128 congruent to n (mod13)

A: Given, 7128≡nmod 13 Find the value of n that satisfies the above congruence.

Q: What sequence of pseudorandom numbers is generated using the pure multiplicative generator xn+1 =…

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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: A phone number is a 7-digit that does not start with 0. Call a phone numbers that make up of exactly…

A: A phone number consists of 7 -digit that does not start with 0. To find the possible phone numbers…

Q: Find the number of permutations without replacement that can be created by drawing 5 balls from a…

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

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Q: What is 2 ^32 mod (5)?

A: mod is the function whose output is always positive. mod is represented by .

Q: Use pigeonhole principle 1. How many numbers must be selected from the set {1, 3, 5, 7, 9, 11, 13,…

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Q: With 100 candidates, find the number of permutations that can be made if 10 beauty queens are…

A: Given total number of candidates, n                 n = 100  Number of beauty queens that are to be…

Q: Apply the Extended Euclidian Algorithm to find 1/21 modulo 59 with a table

A: We will apply Extended Euclidian Algorithm to find 121 modulo 59 i.e., multiplicative inverse of 21…

Q: Find the smallest positive integer for which x mod 3=2 and x mod 4=3   What is the next smallest…

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Q: 5. How many bit strings of length 10 over the alphabet {a, b, c} have either exactly three as or…

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

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

Q: write a program to evaluate even numbers for [1,10],and [11,20]respectively in matlab

A: Even numbers for [1,10] is given below-

Q: Create a proof for the fc

A: Given,           1.        ~R⊃~Q2.        ~R

Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?

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Q: What sequence of pseudorandom numbers is generated using the linear congruential generator Xn+1 =…

A: Given that xn+1=(3xn+465)mod 8191x0=1

Q: 9. Use the algorithm to generate the next 22 permutations of {1,2,3,4,5} starting with 13275.

A: Given: A permuation {1, 2, 3, 4, 5} The algorithm for generating permutation follows an increasing…

Q: Find the order of 4 modulo 49.

A: Evaluate order of 4 modulo 49.

Q: Suppose a password must be express by selecting digits for 5 places, the allowable digits being 0,…

A: Although, the example of a typical password is 332401, a 6 digit number, the first sentence of the…

Q: The order of 5 mod 17 is

A: “Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: The order of 5 mod 17 is *

A: Since ϕ(17) = 16 Therefore order can be the divisor of 16 So the order can be 1,2,4,8 or 16

Q: Show that the set of a+bi Gaussian integers has the same strength as the set of natural numbers N.

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Q: Find a such that 5= 7* modulo 13.

A: Given: 5≡7xmodulo13. The objective is to find the value of x.

Q: 25 Prove that mod 7 5 for all Gindegars and bin b mod 7-6

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Q: If a = 3 (mod12) then a does not equal 1 (mod6)

A: a=b mod n if and only if n divides a-b Now, we have that a=3mod 12 We need to show that a≠1mod 6 Let…

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: Find the order of 5 modulo 31.

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Q: Write down all even permutations of {1,2,3,4} which take the element 1 to 2.

A: To write all even permutation of A={1, 2, 3, 4} that takes 1 to 2.

Q: Give an example of a pair of numbers that can be used to generate modulo residues to represent the…

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Q: What is the smallest positive integer x in the equarion: 1=3x+2(mod 7)?

A: We have to solve the equation 1 = 3x + 2 (mod 7)⇒1 - 2 - 3x = 0 (mod 7)⇒-1 - 3x = 0 (mod 7)⇒3x = - 1…