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40 is the multiplicative inverse
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A. Find the multiplicative inverse of 52 mod 77. Your answer should be an integer s...
8-7. Find the smallest positive integer a such that 5:13 +13n" + a(9) = 0 (mod...
8-7. Find the smallest positive integer a such that 5:13 +13n" + a(9) = 0 (mod 65) for all integers n.
the user should be prompted to enter an integer and then your program will produce another...
the user should be prompted to enter an integer and then your program will produce another integer depending on whether the input was even or odd. The following is an example of what you might see when you run the program; the input you type is shown in green (press Enter at the end of a line), and the output generated by the program is shown in black text. Enter an integer: 1234 Number is even, taking every other digit...
Please answer the following two questions. Find the smallest positive integer solution to the equation. Show...
Please answer the following two questions.
Find the smallest positive integer solution to the equation. Show all of your work. x = 4 mod 7 Find the smallest positive integer solution to the equation. Show all of your work. x5 = 11 mod 35
You may import the following library functions in your module: from fractions import gcd from math...
You may import the following library functions in your module: from fractions import gcd from math import floor from random import randint You may also use: • the built-in pow() function to compute modular exponents efficiently (i.e., ak mod n can be written in Python as pow(a,k,n)), • the sum() function returns the sum of a list of integers (sum(1,2,3,4) returns 10). problem 1 a. Implement a function invPrime(a, p) that takes two integers a and p > 1 where...
Page 2 II. (7) Use the Laplace Transform method to solve the IVP y' - 8y...
Page 2 II. (7) Use the Laplace Transform method to solve the IVP y' - 8y + 16y = 14 y(0) = 1,5/(0) = 4 Show all your work. Note: A partial fraction decomposition will not be needed here if you carefully solve for Y (s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the...
Write a method named factorial that accepts an integer n as a parameter and returns the...
Write a method named factorial that accepts an integer n as a parameter and returns the factorial of n, or n!. A factorial of an integer is defined as the product of all integers from 1 through that integer inclusive. For example, the call of factorial(4) should return 1 2 3 4, or 24. The factorial of 0 and 1 are defined to be 1. You may assume that the value passed is non-negative and that its factorial can fit...
Use the Laplace Transform method to solve the IVP y" - 8y + 16y = t4...
Use the Laplace Transform method to solve the IVP y" - 8y + 16y = t4 y(0) = 1,5(0) - 4. Show all your work Note: A partial fraction decomposition will not be needed here if you carefully solve for Y(s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the coefficient of Y() which will...
Page 2 T Use the Laplace Transform method to solve the IVP 1-8y + 16y-te (0)...
Page 2 T Use the Laplace Transform method to solve the IVP 1-8y + 16y-te (0) = 1,0) = 4 Show all your work. Note: A partial fraction decomposition will not be needed here if you carefully solve for Y(s) = {v}(s), by first moving the expression of the form -as -b with a and b positive integers to the right hand side and then dividing both sides of the equation by the coefficient of Y(8) which will be of...
Please answer question 3 Find all (infinitely many) solutions of the system of congruence's: Use Fermata...
Please answer question 3
Find all (infinitely many) solutions of the system of congruence's: Use Fermata little theorem to find 8^223 mod 11. (You are not allowed to use modular exponentiation.) Show that if p f a, then a^y-2 is an inverse of a modulo p. Use this observation to compute an inverse 2 modulo 7. What is the decryption function for an affine cipher if the encryption function is 13x + 17 (mod 26)? Encode and then decode the...
i. Evaluate the following sum. You must show your work, and your final answer should be...
i. Evaluate the following sum. You must show your work, and your final answer should be a single integer. 84 9k= k=4 ii. Derive a formula in terms of n for the following sum. You must show your work, and your final formula should only contain n and integers (but not k). 8 = k=4 iii. Derive a formula in terms of a and b for the following sum. You must show your work, and your final formula should only...
8-7. Find the smallest positive integer a such that 5:13 +13n" + a(9) = 0 (mod 65) for all integers n.
Please answer the following two questions.
Find the smallest positive integer solution to the equation. Show all of your work. x = 4 mod 7 Find the smallest positive integer solution to the equation. Show all of your work. x5 = 11 mod 35
Page 2 II. (7) Use the Laplace Transform method to solve the IVP y' - 8y + 16y = 14 y(0) = 1,5/(0) = 4 Show all your work. Note: A partial fraction decomposition will not be needed here if you carefully solve for Y (s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the...
Write a method named factorial that accepts an integer n as a parameter and returns the factorial of n, or n!. A factorial of an integer is defined as the product of all integers from 1 through that integer inclusive. For example, the call of factorial(4) should return 1 2 3 4, or 24. The factorial of 0 and 1 are defined to be 1. You may assume that the value passed is non-negative and that its factorial can fit...
Use the Laplace Transform method to solve the IVP y" - 8y + 16y = t4 y(0) = 1,5(0) - 4. Show all your work Note: A partial fraction decomposition will not be needed here if you carefully solve for Y(s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the coefficient of Y() which will...
Page 2 T Use the Laplace Transform method to solve the IVP 1-8y + 16y-te (0) = 1,0) = 4 Show all your work. Note: A partial fraction decomposition will not be needed here if you carefully solve for Y(s) = {v}(s), by first moving the expression of the form -as -b with a and b positive integers to the right hand side and then dividing both sides of the equation by the coefficient of Y(8) which will be of...
Please answer question 3
Find all (infinitely many) solutions of the system of congruence's: Use Fermata little theorem to find 8^223 mod 11. (You are not allowed to use modular exponentiation.) Show that if p f a, then a^y-2 is an inverse of a modulo p. Use this observation to compute an inverse 2 modulo 7. What is the decryption function for an affine cipher if the encryption function is 13x + 17 (mod 26)? Encode and then decode the...
i. Evaluate the following sum. You must show your work, and your final answer should be a single integer. 84 9k= k=4 ii. Derive a formula in terms of n for the following sum. You must show your work, and your final formula should only contain n and integers (but not k). 8 = k=4 iii. Derive a formula in terms of a and b for the following sum. You must show your work, and your final formula should only...
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