4. The factorial of a positive integer n –which we denote as n!-is the product of n and the factorial o -1. The factorial of 0 is 1. Write two different recursive methods that each return the factorial of 1
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- Write code for. Computes the smallest x that satisfies the chinese remainder theorem for a system of equations. The system of equations has the form: x % nums[0] = rems[0] x % nums[1] = rems[1] ... x % nums[k - 1] = rems[k - 1] Where k is the number of elements in nums and rems, k > 0. All numbers in nums needs to be pariwise coprime otherwise an exception is raised returns x: the smallest value for x that satisfies the system of equations.Program the following using SageMath Python:Use Sage ) to write a program that williteratively calculate kR for a point R on an elliptic curve E modulo n where k ≥ 2. You’lluse this program in the elliptic curve method problem on this assignment.• Remember that in the elliptic curve method for factorization, we are actively looking fora ZeroDivisionError, so you might want to use “try—catch” in order to catch this errorif it occurs in the calculation.Which of these statements is true about the following code? int mystery(int n){ if (n>0) return n + mystery(n-1); return 0; } Select one: O a. The base case for this recursive function is an argument with the value zero. O b. There is no base case. O c. The base case for this recursive method is an argument with any value which is greater than zero. O d. The base case for this recursive method is an argument with any value which is less than or equal to zero.
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- please code in python Zeller's congruence is a method to determine the day of the week (e.g., Sunday, Monday, etc.) from a calendar date given the day (d), modified-month (m) and year (y): Note that all division operations in the formula above indicate integer, or truncated division. For example, should be read as (26 * (m + 1)) // 10, not (26 * (m + 1)) / 10. The modified-month value only applies to the months of January and February, which are counted as months 13 and 14 of the previous year: e.g., 13 = Jan, 14 = Feb, 3 = Mar, 4 = Apr, 5 = May, . . . 12 = Dec. For example, 2/21/2014 (Feb 21, 2014) would be represented as 14/21/2013. Also note, algebraic constructs like 26(m + 1) in the equation above must be translated to Python (i.e., 26 *(m + 1) ). Zeller's congruence gives the day of the week starting with 0 = Monday, 1 = Tuesday and so on. Write a program that will input a date as three separate integer values (month, day, and year) and return the day-of-the-week value as…Given a number n, identify and print which in the given set of numbers are factors of n. Should there be no factors listed in the set of numbers, print "I'm alone". For example, given the number 36 and the set of numbers 2, 3, 5, 7, 12. Only print the numbers which are factors of 36, which are 2, 3, 12. Input The first line contains the number n; The second line contains how many numbers there are in the set of numbers; The third line contains the set of numbers. INPUT: 36 5 2·3·5·7·12 Output The set of numbers that are factors of n separated by a new line in order of appearance. If there are none, print "I'm alone" OUTPUT: 2 3 12The nth harmonic number is defined non-recursively as: H(n)=1+1/2+1/3+1/4+...+1/n Come up with a recursive definition and use it to guide you to write a method definition for a double-valued method named “harmonic” that accepts an int parameter n and recursively calculates and returns the nth harmonic number. Write a test program that displays the harmonic numbers, H(n)=1,2,3,4...10
- Write a static recursive method called mrecursiv that displays all of the permutations of the characters in a string passed to the method as its argument. For example, the character sequence abc has the following permutations: acb, bac, bca, cab, cba. Then Write a static method called getInput that get an input string from the user and passed it to the mrecursiv method written above in a method call.: In the classic problem FizzBuzz, you are told to print the numbers from 1 to n. However,when the number is divisible by 3, print "Fizz''. When it is divisible by 5, print "Buzz''. When it isdivisible by 3 and 5, print"FizzBuzz''. In this problem, you are asked to do this in a multithreaded way.Implement a multithreaded version of FizzBuzz with four threads. One thread checks for divisibilityof 3 and prints"Fizz''. Another thread is responsible for divisibility of 5 and prints"Buzz''. A third threadis responsible for divisibility of 3 and 5 and prints "FizzBuzz''. A fourth thread does the numbers.Determine whether a string is a palindromeA palindrome is a string of characters that reads the same from right to left as it does from left to right, regardless of punctuation and spaces.The specifications for this assignment are: •Write and test a non-recursive solution in Java that determines whether a string is a palindrome •Your program should consist of at least two methods: (1) the main method (2) the method which performs the task of determining whether the specified string is a palindrome. You should name this method isPalindrome. You should name the class that contains your “main” method and the isPalindrome method FindPalindrome. •You must use a Stack and a Queue in your solution: Write your own Stack and Queue based on the Vector in the Java API and use those in your solution. You should name those classes StackVector and QueueVector respectively. You already have access to the relevant exception classes and interfaces for the above ADTs. •All of your belong to a Java…