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- Java Find the square root of anumber without using sqrt function . the number msut be taken from user1. A set of integers are relatively prime to each other if there is no integer greater than 1 that divides all the elements. Furthermore, in Number Theory, it is known that the Euler function,ϕ (n), expresses the number of positive integers less than n that are relatively prime with n. Choose the alternative that has the correct value of ϕ(n) for every n below. A) ϕ(5) = 4 B) ϕ(6) = 2 C) ϕ(10) = 3 D) ϕ(14) = 6 E) ϕ(17) = 16Please you neeedUsing recursion to print half of the indent hourglass pattern.
- Find the recursive equation. use telescoping method, transformations and Verify your answerQ4. Recursion Find how many possible combinations that a number can be decomposed into the multiple of integers (smaller than the number itself) by a recursion function.Suppose we have a positive number Y as input, and it need to be decomposed into the multiple of several integers, Yi, where each Yi, is smaller than Y(e.g., Y=Y1∗Y2∗ Y3∗...∗Yn). In addition, these decomposed integers can only be arranged in an ascending order (Y1Use back substitution method to compute the following recursive function. Note that final results must be presented as a function of n. Show at least three substitutions before moving to k steps to get credit.
- (b) Let n be an integer. Show that n if the sum of the digits of n is a multiple of 3,then n is a multiple of 3. You must do so by a direct proof. For this problem youmay assume that ∀a, b ∈ Z, ∀m ∈ Z+, (a ≡ x (mod m) ∧ b ≡ y (mod m)) ⇒ ab ≡ xymod m. *Solve by direct proof*3. Largest: a recursive function that computes the largest value for an integer array of positiveand negative values. For example, for the array below, the function largest should return 22,which is the largest value in the array. You can assume there are no more 20 integers in thearray. Think of how to formulate the recurrence relation in this problem yourself.ce from the user t using recursion.
- How do I code Fibonacci Function in C program? I need to only print out by 5 each Fibonacci number (0, 5, 10, 15, 20, 25, 30, 35, 40, 45). This is associated with recursion, while a direct code solution exists using loops, recursion needs to be used.Create a limit evaluation problem that requires substitution with an answer of 1. Please show the steps to solve the problem.Create a Mathpy program that solves a 3x3 and 4x4 matrix via Gaussian Elimination Method and Back Substitution. The program must be able to display every change in the Matrix.