Implement a Python method fft25Z(a, W) adapted from CLRS's RECURSIVE-FFT and use it to multiply the above p(x) and q(x) ∈ Z[257][x]. Unlike RECURSIVE-FFT, where the arithmetic is carried out in the complex numbers, here all the arithmetic is to be done in 7257*. Specifically:
a) assuming that degree (p) + degree (q) < 8, first give without justification: Give an 8th root of unity W in Z257. ii. Give its inverse W^(-1) in Z257. iii. Give the inverse 8^(-1) of 8 modulo 257.