The goal of this exercise is to work thru the RSA system in a simple case: We will use primes p = 71, q = 61 and form 71 · 61 = 4331. n = [This is typical of the RSA system which chooses two large primes at random generally, and multiplies them to find n. The public will known but p and q will be kept private.]

Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies.   Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you fill in the values is the correct one. Notice how it is a lot easier to analyze the running time of…

Use google Colaboratory

What do I do for (K + 1)? Please explain as best as possible

More and more seafood is being farm-raised these days. A model (differentialequation) used for the rate of change for a fish population, P(t) in farmingponds is given by P'(t) = b(1-(P(t)/Pm)) - hP(t) where b is the birth rate, PM is the maximum number of fish the pond cansupport, and h is the rate the fish are harvested. Write a python code that implements the Forward Euler method to solve thedifferential equation Suppose that the carrying capacity PM = 20, 000 fish with a birth rateof 6% and a harvesting rate of h = 0%, use your Python code to findand plot the numerical solution for the first 400 days for different valuesof y0. Pick y0 < 20, 000, y0 > 20, 000. Don’t forget to label all your plotswith x and y axes label, titles and legends. Use a time step ∆t = 0.1

For which value(s) of x ∈R is the following statement false? Why? If |x −3|= 1, then |x −2|= 2.   Please give proper explanation and typed answer only.

5. Practice with RSA algorithma. Pick two prime numbers p, q, for example,• const int P=23;• const int Q=17;• int PQ=P*Q; b. Find a e that is relatively prime with (p-1)(q-1)Call RelativelyPrime () c. Calculate the inverse modulo (p-1)(q-1) of e to be your dUse inverse ()   c++