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The first Hardy-Littlewood conjecture is called the k-tuple conjecture. It states that the asymptotic number of prime constellations can be computed explicitly. A particular ...

A dual number is a number x+epsilony, where x,y in R and epsilon is a matrix with the property that epsilon^2=0 (such as epsilon=[0 1; 0 0]).

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 thickness (or depth) t(G) (Skiena 1990, p. 251; Beineke 1997) or theta(G) (Harary 1994, p. 120) of a graph G is the minimum number of planar edge-induced subgraphs P_i of ...

Given a simple harmonic oscillator with a quadratic perturbation, write the perturbation term in the form alphaepsilonx^2, x^..+omega_0^2x-alphaepsilonx^2=0, (1) find the ...

The quartic surface given by the equation x^4+y^4+z^4-(x^2+y^2+z^2)=0.

At least one power series solution will be obtained when applying the Frobenius method if the expansion point is an ordinary, or regular, singular point. The number of roots ...

For every positive integer n, there exists a sphere which has exactly n lattice points on its surface. The sphere is given by the equation ...

The quartic formula is a name sometimes given to one of the related explicit formulas for the four roots z_1, ..., z_4 of an arbitrary quartic equation with real coefficients ...

A weak snark is a cyclically 4-edge connected cubic graph with edge chromatic number 4 and girth at least 4 (Brinkmann et al. 2013). Weak snarks therefore represent a more ...