4. (a) Show that if n is any integer, then precisely one of n – 1, n, and n +1 is divisible by 3. Hint. Use the division algorithm.

Q: Consider the division algorithm a, bEZ such that b-6. Then alat1)(2a+1) 6.

A: Given that a, b belongs to set of integers means a and b are integers.  Where b = 6 As we know that,…

Q: 1. a. Use the division algorithm to prove that given any odd integer n, there is an integer k for…

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Q: Use Euclid’s algorithm to determine whether 100−1 exists in Z2121 and to find it if it does exist

A: The euclid algorithm states that, If gcd(m,n)=1 Then remainder for m is n. If gcd(m,n)≠1, gcd(m,n=r…

Q: 4. (a) Show that if n is any integer, then precisely one of n – 1, n, and n+1 is divisible by 3.…

A:

Q: Suppose that each person in a group of n people votes forexactly two people from a slate of…

A: According to the given information, For part (a) Each people in a group of n people votes for…

Q: (Discrete Math) Use Euclid’s algorithm to calculate gcd(33+35,33²+35²).

A: The GCD of a pair of a number can be calculated using Euclid's algorithm. The algorithm uses a…

Q: a. Write an algorithm to find the smallest and largest numbers in an array. b. Using Induction,…

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Q: a. Write an algorithm to find the smallest and largest numbers in an array. b. Using Induction,…

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Q: 3. Write a recursive algorithm of the sequence t(1)=-1 and t(n)=5x t(n-1)+n² as a function.

A:

Q: A student is allowed to select at most n books from a collection of (2n+1) books. If the total…

A: We will solve the problem

Q: T Use base-ten pieces to illustrate the long-division algorithm. In separate steps, show which…

A:

Q: a) Simplify the expression [p^ (p→ q )] → q by using the laws of logic. b) Write an Algorithm for…

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Q: use the discrete Putzer algorithm to evaluate A". [1 2 -1] 0 5 A = 0 1 -4 The question of Difference…

A: Concept: Putzer's algorithm : The differential equation dx dt = Ax where A is a fundamental matrix…

Q: ) Show that ifn is any integer, then precisely one of n – 1, n, and n+1 is divisible by 3. Hint. Use…

A: I shall solve first question only as you have asked more than one unrelated problems. For others…

Q: 4. Explain why if p is prime then Z, is the only subdomain of Z,

A: To prove:If p is prime, Zp is an subdomain(internal domain).

Q: 3. Use the inversion algorithm to find A, [2 1 -2] A = 0 3 li 2 3.

A: We have to find the inverse of the matrix A

Q: Number theory

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Q: Which of the facts/claims were used to justify the Euclidian Algorithm? Choose all that apply. O…

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Q: Use base-ten pieces to illustrate the long-division algorithm. In separate steps, show which…

A: NOTE: In explanation below, 'tens' and 'longs' are referred to same place hence used…

Q: 5 (9 9 () 2. Find a reduced residue system modulo 2", where m is a positive integer. in a reduced…

A: To find a reduced residue system modulo 2m, where m is a positive integer.

Q: 2.4 a. Find all the cluster points of the set Q of all rational numbers, and justify your…

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Q: When we multiply 38 × 73 using the standard algorithm, we start the second row by writing a zero, as…

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Q: a. Write an algorithm to find the smallest and largest numbers in an array. b. Using Induction,…

A:

Q: (a) How many arrangements of the letters in COMBINATORICS have no con- secutive vowels? (b) In how…

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Q: Suppose that N = pq, where p, q are primes of roughly the same size. a) Show that o(N) can be…

A: As per bartleby guidelines for more than three subparts in a question only first three should be…

Q: 3. According to the Division Algorithm, when 8884113 is divided by 547 a. The quotient is b. The…

A:

Q: For the RSA algorithm with a large n, explain why Bob can calculated from n, but Eve cannot.

A: Hint: We need to discuss that what technique Bob is using.

Q: I. Apply the Division Algorithm on the following pairs of integers. 2. a = 46 and b= -21 %3D 3. a =…

A: We should remember ,remainder  is always non-negative.

Q: Use base-ten pieces to illustrate the long–division algorithm. In separate steps, show which…

A: Here we have to divide 328 by 4   now, when 328 is divided by 4, 82 is the quotient and we het 0 as…

Q: In trying use the Sieve of Eratosthenes find all prime numbers less than 300, when do we stop the…

A: Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given…

Q: Evaluate the advantage and disadvantage of k-NN Algorithm

A:

Q: Let p(n, k) be the number of ways to write the integer n as a sum of exactly k positive integers. A…

A: Consider the given: Number of ways to write the integer n as a sum of exactly k positive…

Q: Use the Division Algorithm to prove that for all positive integers, n,6|(n(n + 1)(2n + 1)).

A: We need to prove that, for all positive integers n, 6 is a factor of the expression given below.

Q: 1 Use Gauss-Jordan algorithm to find eAt for A -21

A: Use the following formula, to obtain the solution. If the eigenvalue λ has multiplicity 2, then the…

Q: # 1. Using the extended Euclidean algorithm, calculate integers s and t such that 63s+49t =…

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Q: Consider the following algorithm segment. Assume that n is a positive integer. for i: = 1 to 4n s:=…

A: Given:

Q: MK18. Show that in any set of 9 integers chosen from the set {2,3, 4, ... , 21, 22}, there are at…

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Q: 12. Compute each of the following using the counting-up algorithm. a. 74 63 - b. 73 - 57

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Q: What is the largest n such that 16 and 25 are in the same remainder class modulo n? Write out the…

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Q: 2. (a) Prove by induction : 3+7+11+.. .+(4n-1) = n(2n+ 1) %3D (b) Write an algorithm to find the sum…

A: a) 3+7+11+....+(4n-1)=n(2n+1)b) algorithm to find sum of first five natural numbers.

Q: a. Write an algorithm to find the smallest and largest numbers in an array. b. Using Induction,…

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Q: 5. Suppose we have an enumeration of A ao, a1, A2, ·.. (1) without repetitions (i.e., all the a; are…

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Q: If you are using the Sieve of Eratosthenes to find all the prime numbers between 50 and 150, how…

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Q: 8. Make sketches of work with base-ten materials to support the usual algorithm for calculating each…

A: Note: Since the question contains multiple subparts, as per our policy we are only allowed to solve…

Q: Consider the following algorithm segment. Assume that n is a positive integer. for i:= 1 to n for…

A: given algorithm segment , for i:=1 to n    for j:=[(i+1)/2] to n        x:= i . j      // here is…

Q: 13 The quotient and the remainder according to the division algorithm when n is divide by m, where n…

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Q: NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to…

A:

Q: How many times will the innermost loop be iterated when the algorithm segment is implemented and…

A: 1) i greater equal to (>=) j  2) j greater equal to (>=) k  3) k greater equal to (>=) 1.…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.