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x->x^2$x\mapsto x^2$ is a (1-1) automorphism on fields of characteristic 2, whereas it is 2-1 on F_q{0}$F_q\setminus{0}$ if q is odd. Not a high level concept, but this is where all things quadratic (reciprocity, residues, etc.) break down.
x->x^2 is a (1-1) automorphism on fields of characteristic 2, whereas it is 2-1 on F_q{0} if q is odd. Not a high level concept, but this is where all things quadratic (reciprocity, residues, etc.) break down.
$x\mapsto x^2$ is a (1-1) automorphism on fields of characteristic 2, whereas it is 2-1 on $F_q\setminus{0}$ if q is odd. Not a high level concept, but this is where all things quadratic (reciprocity, residues, etc.) break down.
x->x^2 is a (1-1) automorphism on fields of characteristic 2, whereas it is 2-1 on F_q{0} if q is odd. Not a high level concept, but this is where all things quadratic (reciprocity, residues, etc.) break down.
