Exercise
Consider the polynomial d = X2 + 1 in Z/2Z[X]. Three of the following polynomials are in the same residue class modulo d. Which one is the exception?
f1 = 1 + X + X3 +X4.
f2 = 1 + X + X2 +X3 + X4.
f3 = (1 + X)2.
f4 =
1 + X + X2 +X3.
No. f1 mod d = 0.
Yes. f2 mod d = 1.
No. f3 mod d = 0.
No. f4 mod d = 0.