Quadraticresidues: Half of the nonzero residuesmodulo an odd prime p.
Euler's criterion: A quadraticresidue raised to the power of (p-1)/2 is 1.
In particular, g itself can't be a quadraticresidue (the order of g must be p-1, and it would be at most (p-1)/2 if g was congruent to the square of some x, since the order of x divides p-1, by Fermat's little theorem).
In mathematics, a quadratic equation is a polynomial equation of the second degree.
Quadratic equations are called quadratic because quadratus is Latin for "square"; in the leading term the variable is squared.
For quadratic equations with integer coefficients, if the discriminant is a perfect square, then the roots are rational numbers—in other cases they may be quadratic irrationals.
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