In the RSA, Bob is considering the following choices for the values of p,q and e: p = 13, q =5, e = 3 p = 11, q = 11, e = 3 p = 11, q = 31, e = 5 For each choice determine whether it is correct or not and justify/ prove your answer to the greatest extent. After thinking a little bit more, Bob chooses p = 5, q = 11 and e = 7 i) determine the values of n and φ(n). (ii) Determine d.  (iii) Encrypt M = 2.

Q8 PPLZ,

Consider the following program, in which a, b, and c are the last 3 digits of your student ID number (for example, if you student ID is 170123456, then you should substitute 4 for a, 5 for b, and 6 for c in the program): maximise axı + 3x2 + x3 subject to -bx1 – x2 + 2x3 > 6 -x2 + x3 = 1 - cx1 + 2x2 – 2x3 0 (i) Give the initial starting tableau for the 2-phase simplex algorithm for this program. (ii) Carry out the 2-phase simplex algorithm on this problem. You should give an optimal solution to the program or say why an optimal solution does not exist. Show your work and explain how you determined if the program is feasible or not at the end of the first phase.

What is the correct way to check whether a variable x is divisible by 3 and divisible by 2 but not divisible by 5?     if( (x%3 && x%2 && !x%5)     if( (x%3 ==0) && (x%2 ==0) && !(x%5 ==0))     if( (x%3 ==0) && (x%2 ==0) ^ (x%5 ==0))     if( (x%3 ==0) && (x%2 ==0) || !(x%5 ==0))