Find the expansion base 3 of 54. Ex: 1010
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- The GMP library, using C or C++ The prefered solution is to use the Sage library. 2 Fermat test 1. Implement the Fermat test of primality with small integers. 2. Write a function to generate random k-bit prime numbers. 3 RSA 1. Write the key-generation function function of RSA. The function should generate two random primes p and q of size k/2 bits. 2. Implement the RSA encryption function 3. Implement the RSA decryption function 4. Check that decryption worksAnswer it is c++ only Chef recorded a video explaining his favorite recipe. However, the size of the video is too large to upload on the internet. He wants to compress the video so that it has the minimum size possible. Chef's video has N frames initially. The value of the th frame is A₁. Chef can do the following type of operation any number of times: • Choose an index i (1 ≤ i ≤ N) such that the value of the ith frame is equal to the value of either of its neighbors and remove the ith frame. Find the minimum number of frames Chef can achieve. Input 1 1 5 output 1: An array A contains all the integers from O to n, except for one number whichis missing. In this problem, we cannot access an entire integer in A with a single operation. Theelements of A are represented in binary, and the only operation we can use to access them is "fetchthe jth bit of A[i];' which takes constant time. Write code to find the missing integer. Can you do itin O(n) time?
- t) The speed of RSA hinges on the ability to do large modular exponentiations quickly. While e can be made small, d generally cannot. A popular method for fast modular exponentiation is the Square and Multiply algorithm. Suppose that N 4961. We want to use the Square and Multiply algorithm to quickly decrypt y = 7475. a) Express d as a binary string (e. g. 10110110). = 8453 and d = b) Supposing that initially r = y = 7475, enter the order of square operations (SQ) and multiply operations (MUL) that must be performed on r to compute yd mod N. Enter as a comma separated list, for example SQ, MUL, SQ, SQ, SQ, MUL, SQ, SQ, MUL, SQ, SQ c) What is x = yd mod N?3. For n No let w(n) denote the number of 1s in the binary representation of n. For example, w (9) = 2, since $9$ is 1001 in binary. Try to find a closed formula for g(n) in terms of n and w(n). If you succeed, the following question will be very easy. 10000000000000011 in binary notation. What is g(n)? Write your answer in binary! Let n =Note: Solution needed in Languare : JAVA Version: 8 A non-negative integer N is called sparse if its binary representation does not contain two consecutive bits set to 1. For example, 41 is sparse, because its binary representation is "101001" and it does not contain two consecutive 1s. On the other hand, 26 is not sparse, because its binary representation is "11010" and it contains two consecutive 1s. Two non-negative integers P and Q are called a sparse decomposition of integer N if P and Q are sparse and N = P + Q. For example: 8 and 18 are a sparse decomposition of 26 (binary representation of 8 is "1000", binary representation of 18 is "10010"); 9 and 17 are a sparse decomposition of 26 (binary representation of 9 is "1001", binary representation of 17 is "10001"); 2 and 24 are not a sparse decomposition of 26; though 2 + 24 = 26, the binary representation of 24 is "11000", which is not sparse. Write a function: def solution(N) that, given a non-negative integer N, returns any…
- = = 2×2 and 6 = (a) A composite number is a positive integer that has at least one divisor other than 1 and itself. For example, 2 1×2 is not a composite number but 4 2 × 3 are composite numbers. A logic circuit has four binary input variables, A, B, C and D. The output Z of the logic circuit is 1 if the unsigned integer represented by the binary number ABCD is a composite number. Using variables A and B for the select inputs S1 and S0 of a 4-to-1 multiplexer, implement the logic function Z(A, B, C, D) using this multiplexor and other logic gates.Decrypt a message that was encrypted using the following logic: • First the words in the sentence are reversed. For example, "welcome to hackerrank" becomes "hackerrank to welcome" • For each word, adjacent repeated letters are compressed in the format <character><frequency>. For example, "mississippi" becomes "mis2is2ip2i" or "baaa" becomes "ba3". Note the format is not applied for characters with frequency 1. Also, the frequency will be no greater than 9 Return the decrypted string Exampl e..2.ampleQuestion Give the array that results after applying Dijkstra's 3-way partitioning subroutine from lecture to the following array: 42 76 42 28 42 61 42 88 17 77 Answer Your answer should be a sequence of 10 integers, separated by whitespace.
- Transcribed Image Text You are given a sequence of 16N positive integers a1, a2, . .. , a16N - You may shuffle this sequence in any way you choose, i.e. change it to any one of its permutations. Then, let (a1 Đ a2) ® (az e a4) ...® (asN-1 asN), (a8N+1 O a8N+2) ® (asN+3 O a8N+4) ®...® (a16N-1 O A16N), where O and O denote bitwise AND and XOR respectively. Find the maximum possible value of x – yA certain company has encoded the accounts of its customers and requires that you provide an algorithm that, given an account code, informs if it is valid according to the following description: The account codes are made up of 4 digits counted from right to left, plus the verification digit. The verifying digit is obtained by adding the digits of the account number of the even positions and multiplying the digits of the odd positions, from the new result the residue of the division is extracted for 10, which represents the verifying digit. Develop the code in python as a check digit class that returns 1 if it is correct or 0 if not Heading: Extract digits, verifier calculation, Account verification, Integral algorithm Code in python no use chat gptA certain company has encoded the accounts of its customers and requires that you provide an algorithm that, given an account code, informs if it is valid according to the following description: The account codes are made up of 4 digits counted from right to left, plus the verification digit. The verifying digit is obtained by adding the digits of the account number of the even positions and multiplying the digits of the odd positions, from the new result the residue of the division is extracted for 10, which represents the verifying digit. No use CHATGPT Develop the code in python as a check digit class that returns 1 if it is correct or 0 if not