Search Results for ""

Gauss stated the reciprocity theorem for the case n=4 x^4=q (mod p) (1) can be solved using the Gaussian integers as ...

If there is an integer x such that x^4=q (mod p), then q is said to be a biquadratic residue (mod p). If not, q is said to be a biquadratic nonresidue (mod p).

A quaternion with complex coefficients. The algebra of biquaternions is isomorphic to a full matrix ring over the complex number field (van der Waerden 1985).

A transformation in which coordinates in two spaces are expressed rationally in terms of those in another.

Let T be an ergodic endomorphism of the probability space X and let f:X->R be a real-valued measurable function. Then for almost every x in X, we have 1/nsum_(j=1)^nf ...

In homogeneous coordinates, the first positive quadrant joins (0,1) with (1,0) by "points" (f_1,f_2), and is mapped onto the hyperbolic line -infty<u<+infty by the ...

Let A and B be two algebras over the same signature Sigma, with carriers A and B, respectively (cf. universal algebra). B is a subalgebra of A if B subset= A and every ...

Two adjoined rotundas.

Birthday attacks are a class of brute-force techniques used in an attempt to solve a class of cryptographic hash function problems. These methods take advantage of functions ...

Consider the probability Q_1(n,d) that no two people out of a group of n will have matching birthdays out of d equally possible birthdays. Start with an arbitrary person's ...