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N_phi(m) is the number of integers n for which the totient function phi(n)=m, also called the multiplicity of m (Guy 1994). Erdős (1958) proved that if a multiplicity occurs ...

The truncated dodecadodecahedral graph is the skeleton of the truncated dodecadodecahedron, which is the only uniform polyhedron for which this is the case. It will be ...

The j-function is the modular function defined by j(tau)=1728J(tau), (1) where tau is the half-period ratio, I[tau]>0, ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

If an n-sided Poncelet transverse constructed for two given conic sections is closed for one point of origin, it is closed for any position of the point of origin. ...

The constant pi, denoted pi, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r, pi = C/d (1) = C/(2r) (2) pi has decimal expansion ...

A finite group is a group having finite group order. Examples of finite groups are the modulo multiplication groups, point groups, cyclic groups, dihedral groups, symmetric ...