An integer n is called k-perfect if u(n) =kn. Note that a perfect number is 2-perfect. Show that 120 = 23 • 3 · 5 is 3-perfect.

Q: T(n)=7T(n/2)+n, where T (1)=1 b. Use induction to prove your result. Use induction to prove the…

A: Suppose n is a power of 2, say n=2^k, and suppose T(1)=1. ThenT(n)=7T(n/2)+n…

Q: How many three-letter "words" can be made from 6 letters FGHIJK" if repetition of letters (a) is…

A: Given: 6 letters are "FGHIJK"   (a) To form three-letter words for which repetition is allowed.…

Q: There are n ≥ 2 married couples who need to cross a river. They have a boat that can hold no more…

A: Set the number of couples (n) to 2. Set the boat's starting bank (boatBank) to 1. Set the starting…

Q: Order the functions in increasing order

A: Given functions are: n2, n3, n!, nlog2n, n2, nlog10n, 3n, (log2 n)*(log2 n)

Q: Consider the set of integers. 1. Use a direct proof to show that the sum of two even integers is…

A: 1. Use a direct proof to show that the sum of two even integers is even. Solution: let assume x and…

Q: Let P(n) be the statement that a postage of n cents can be formed using just  4-cent and 5-cent…

A: Lets see the solution of the above problem.

Q: Given a list of n positive integers, show that there must two of these integers whose difference is…

A: - We need to show that there must be two integers in a n length list whose difference is divisible…

Q: A string is called "s-palindrome" if it is symmetric about the middle of the string. For example,…

A: To write a python program to show that a given string is palindrome or not, if it is symmetric about…

Q: Sahil is an outstanding entertainer. He is expert in what he does. At a day, he accepted Samir's…

A: Algorithm:  First we have to take the input for the test case Then we have to take the value of the…

Q: Ouestion3. Prove the following inequality by induction n< 2", n e Z+

A: Here, I have provided the proof for given inequality by induction. In Mathematical Induction method,…

Q: Find a regular expression for the set {a"bm:(n + m) is even}.

A: Given: We are given a language L = { a^nb^m : (n+m) is even} Goal: To find the regular expression…

Q: Prove the following statement by contraposition. For every integer x, if 5x 2 – 2x + 1 is even, then…

A: Proof for every integer x, if 5x2 – 2x + 1 is even, then x is odd.

Q: Fill in the blanks  1. The --------- of a number is defined to be the power to which some positive…

A: Dear student, As per our guideline we can answer only first three questions. Please repost rest of…

Q: (p → (q A -q)) → →p = Op+q -p OF Op O None of the choices

A: AND (∧) - If A and B two proposition then (A∧B) is true if both the propositions are true. Negation…

Q: Algorithm for Conversion from an Arabic number to a modern Roman number. in: decimal number n (0 ≤…

A: constant: sequence P =
1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1 of primitive Roman…

Q: Let a and b be integers. Then a divides b if and only if: O ab-k for som integer k O you can't…

A: Answer is in next step.

Q: Please help me with computer science programming question.

A: Required:

Q: e integer n, greater than 1, assign True to is_prime if n has no fators other than 1 and itself.…

A: The function is_prime take an integer ,count the number of factors from 1 to n . If the number of…

Q: Let n EN be a natural number with a divisor d E N. If the sum of all of the positive divisors of n…

A: #note: Since programming language is not specified, we are providing answer in python #function to…

Q: A particular random number generator is able to give a bunch of random integers from 0 to 65535. How…

A: Let's see the solution in the next steps

Q: You are given two positive integer groupings a1,… ,an and b1,… ,bm. For each j=1,… ,m track down the…

A: Here have to determine about the Row GCD programming problem statement.

Q: A. Let m, n are integers. Use a proof by contraposition to prove that if m*n is even, then m is even…

A: Proof by contrapositive is a method of proof that is similar to proof by contradiction. It is a…

Q: write oop find result x!+power(x,y) if x in class a and y in class b

A: // Code class A{    public int x=5;}class B{    public int y=3;} public class Main{ public static…

Q: L₁ = {a"ba": n ≥ 0,m>0} Use the rule of contradiction, prove that following language is regular or…

A: I have given written solution of the above problem. See below steps.

Q: Suppose that a “word” is any string of seven letters of the alphabet, with repeated letters allowed.…

A: Given, Suppose that a “word” is any string of seven letters of the alphabet, with repeated letters…

Q: We are interested to see divisibility checking of only prime numbers in base 10. For a prime P, you…

A: The complete code is given below with output .

Q: Let n be an integer. If 3n+ 4 is odd, then n is odd.

A: even*even=even even*odd=even odd*even=even odd*odd=odd   odd+even=odd even+odd=odd even+even=even…

Q: Find a regular expression for the set {a"b": n> 3,m is even}.

A: Given: Find a regular expression for the set {a^n b^m: n ≥ 3,m is even}.

Q: Compute the first four partial sums S1, .., S4 for the series having n th term a, starting with n =…

A: - We have to get the partial sums of the values created from the equation. - The equation for values…

Q: decimal number has a base k same. The singular digits of a base k number are called k-its. How about…

A: Here have to determine about singular digits of a base k number problem statement.

Q: Prove: For all integers n, if n² is odd, then n is odd. Use a proof by contraposition, as in Lemma…

A: For all integers n, if n² is odd, then n is odd. Use a proof by contraposition ?

Q: Prove that for all integers n, if n+1 is divisible by 5, then n² is not divisible by 5. Hint:…

A:

Q: Find the first three examples of an odd number x>0 and an even number y>0 such that x − y = 7.

A: In step 2, I have provided  ANSWER  with BRIEF  EXPLANATION---------------