An organization of 10 individuals is using Shamir Secret Sharing to protect their private data. The quorum they have decided to use is 4, and theyre working (mod 17). 5 members of the team come together to reveal the secret, and reveal the following information:

f(1) = 0, f(5) = 5, f(6) = 5, f(8) = 10, f(10) = 6

(a) What is the minimum number of equations that we need to solve in order to recover the secret a0?

(b) Write down a system of linear equations that, if solved simultaneously, would let us recover the secret a0