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A biquadratic number is a fourth power, n^4. The first few biquadratic numbers are 1, 16, 81, 256, 625, ... (OEIS A000583). The minimum number of biquadratic numbers needed ...

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 ...