Thank you Professor, your videos have been extremely helpful; your series on finite fields and polynomial arithmetic are an excellent companion to Proakis & Salehi's Digital Communications. The test as it is implemented in the latter half of the video works great as far as I can tell. However there may be an inconsistency on the whiteboard @ 3:03 and @ 4:15. From my understanding we should test for *a ² ^ ᵈᵉᵍ⁽ᵖ⁾ ⁻ ¹ ≡ 1 (mod p)* rather than *a ᵈᵉᵍ⁽ᵖ⁾ ⁻ ¹ ≡ 1 (mod p)* Grateful for your help and guidance!
Regarding function: GF_2_isIrreducible_Fermat(), there are 2^(N-1) polynomials of lower order than a polynomial of degree N. How does choosing 10 (or a million or even a billion depending on N) random polynomials test whether f is ACTUALLY irreducible? If the function returns false, then we've found a counter example. But if it returns true, we haven't proven anything. I'm particularly interested in testing for primality of polynomials up to an order of 64, and 2^64 is about 18 quintillion. Hoping not to have to exhaustively test.
