lcg(a,b,m,R0) uses this formula:

Ri+1 = (aRi + b) (mod m) i 0

we need to answer these two questions based on that formula:

I just need the formula to get a and b from two equations of the form:

R1 = (a R0 + b) mod m

R2 = (a R1 + b) mod m if I know R0, R1, R2 and m I need to be able to find a and b

Problem 3 Short answer: An LCG with 16 generates the numbers R 2, R2 11, and Rs 8. Determine the values of a, b, and R. Include your solution, including all relevant work and explanation, in your a3.pdf. Problem 4 In problem 3, you were able to "hack" an LCG by obtaining the values of a and b and thus predict all of its future output (you predicted R4, but of coursc, since a and b are fixed, you could predict any quantity of future valucs). In this problem, you will automate this process. Write a module "a3p4." containing a function "crack-leg(m. ri, r2, r3)", where m is a positive integer, and rl, r2, and r3 are integers between 0 and m -1, inclusive. This function should return a list [a,b], where a and b are the keys for an LCG, with modulus m, which outputs r1, r2, and r3 as its first three random numbers (i.e. rl- Ri, r2- R2, and r3R) Note that in some cases, there may not be a solution. In that case, output the list (0,0] (ie, report a =-0). your program should Problem 3 Short answer: An LCG with 16 generates the numbers R 2, R2 11, and Rs 8. Determine the values of a, b, and R. Include your solution, including all relevant work and explanation, in your a3.pdf. Problem 4 In problem 3, you were able to "hack" an LCG by obtaining the values of a and b and thus predict all of its future output (you predicted R4, but of coursc, since a and b are fixed, you could predict any quantity of future valucs). In this problem, you will automate this process. Write a module "a3p4." containing a function "crack-leg(m. ri, r2, r3)", where m is a positive integer, and rl, r2, and r3 are integers between 0 and m -1, inclusive. This function should return a list [a,b], where a and b are the keys for an LCG, with modulus m, which outputs r1, r2, and r3 as its first three random numbers (i.e. rl- Ri, r2- R2, and r3R) Note that in some cases, there may not be a solution. In that case, output the list (0,0] (ie, report a =-0). your program should