Question

Find the inverse of (x^7+x+1) modulo (x^8 + x^4 + x^3+ x + 1).

(a) x^7+x

(b) x^6+x^3

(c) x^7

(d) x^5+1

I have been asked this question in a job interview.

My question is taken from Polynomial and Modular Arithmetic- III topic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

Answer 1

Correct option is (c) x^7

For explanation I would say: Finding the inverse with respect to (x^8 + x^4 + x^3+ x + 1) we get x^7 as the inverse.