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A number D that possesses no common divisor with a prime number p is either a quadratic residue or nonresidue of p, depending whether D^((p-1)/2) is congruent mod p to +/-1.

The extended complex plane is the name given to the complex plane with a point at infinity attached: C union {infty^~}, where infty^~ denotes complex infinity. It is also ...

Since |(a+ib)(c+id)| = |a+ib||c+di| (1) |(ac-bd)+i(bc+ad)| = sqrt(a^2+b^2)sqrt(c^2+d^2), (2) it follows that (a^2+b^2)(c^2+d^2) = (ac-bd)^2+(bc+ad)^2 (3) = e^2+f^2. (4) This ...

Consider a symmetric triangle wave T(x) of period 2L. Since the function is odd, a_0 = 0 (1) a_n = 0, (2) and b_n = (3) = (32)/(pi^2n^2)cos(1/4npi)sin^3(1/4npi) (4) = ...

Two geometric figures are said to exhibit geometric congruence (or "be geometrically congruent") iff one can be transformed into the other by an isometry (Coxeter and ...

Regardless of where one white and one black square are deleted from an ordinary 8×8 chessboard, the reduced board can always be covered exactly with 31 dominoes (of dimension ...

The cube of a graph is defined as its third graph power.

The dual of the great truncated cuboctahedron U_(20) and Wenninger dual W_(93).

800 The dual of the great rhombidodecahedron U_(73) and Wenninger dual W_(109).

A dozen dozen, or the square number 144.