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Let p>3 be a prime number, then 4(x^p-y^p)/(x-y)=R^2(x,y)-(-1)^((p-1)/2)pS^2(x,y), where R(x,y) and S(x,y) are homogeneous polynomials in x and y with integer coefficients. ...

The gnomonic projection is a nonconformal map projection obtained by projecting points P_1 (or P_2) on the surface of sphere from a sphere's center O to point P in a plane ...

The graph neighborhood of a vertex v in a graph is the set of all the vertices adjacent to v including v itself. More generally, the ith neighborhood of v is the set of all ...

The great rhombidodecahedron is the uniform polyhedron with Maeder index 73 (Maeder 1997), Wenninger index 109 (Wenninger 1989), Coxeter index 89 (Coxeter et al. 1954), and ...

There are two different statements, each separately known as the greatest common divisor theorem. 1. Given positive integers m and n, it is possible to choose integers x and ...

Let sigma(n) be the divisor function. Then lim sup_(n->infty)(sigma(n))/(nlnlnn)=e^gamma, where gamma is the Euler-Mascheroni constant. Ramanujan independently discovered a ...

A group automorphism is an isomorphism from a group to itself. If G is a finite multiplicative group, an automorphism of G can be described as a way of rewriting its ...

The group direct sum of a sequence {G_n}_(n=0)^infty of groups G_n is the set of all sequences {g_n}_(n=0)^infty, where each g_n is an element of G_n, and g_n is equal to the ...

A group homomorphism is a map f:G->H between two groups such that the group operation is preserved:f(g_1g_2)=f(g_1)f(g_2) for all g_1,g_2 in G, where the product on the ...

The half-Moses circle is defined as the circle having the same center as the Moses circle, i.e., the Brocard midpoint X_(39) but half its radius, i.e., R_H = ...