We wish to use the AKS algorithm to test whether 211 is a prime number. PLEASE see the wikipedia reference for a concise explanation of AKS primality test.

a) Use a computer to compute if (x + a)²¹¹ = x²¹¹+ a (mod 211) for a suitable choice of a. Be sure to explain why your choice of a is allowed. Does this allow us to conclude that 211 is prime?

b) Compute the value r as detailed in the AKS algorithm. I.e., this is the exponent such that we will compute (x + a)²¹¹ (mod x^r - 1).

Note: Please only answer this question if you actually understand the AKS primality test