<Dl> <Dd> b a (R (a c b 2) + 1). (\ displaystyle (\ frac (b) (a)) \ left (R \ left ((\ frac (ac) (b ^ (2))) \ right) + 1 \ right).) </Dd> </Dl> <Dd> b a (R (a c b 2) + 1). (\ displaystyle (\ frac (b) (a)) \ left (R \ left ((\ frac (ac) (b ^ (2))) \ right) + 1 \ right).) </Dd> <P> For example, let a denote a multiplicative generator of the group of units of F, the Galois field of order four (thus a and a + 1 are roots of x + x + 1 over F. Because (a + 1) = a, a + 1 is the unique solution of the quadratic equation x + a = 0 . On the other hand, the polynomial x + ax + 1 is irreducible over F, but it splits over F, where it has the two roots ab and ab + a, where b is a root of x + x + a in F . </P> <P> This is a special case of Artin--Schreier theory . </P>

Where did the term second nature come from