Let p = 1621, it is given that 17 is a generator of (Z*_p, ). Let. B = {2, 3} be a factor base (as in the index calculus method). Find at least two distinct equations of the form 17^k 2^e3^t mod p for some integers k, e, t. Let B = {2, 3, 5, 7, 11, 13, 17, 23} be another factor base. in this case, find at least 8 distinct equations of the form 17^k = 2^i3^t5^b7^y11^o13^u17^s23^j for some integers k, i, t, b, y, o, u, s, j. Discuss advantages and disadvantages of using larger factor base. Note 7 in (Zp, ) has order 81. What do you think about, using 7 instead of 17 in part a and part b