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For elliptic curves over the rationals Q, the group of rational points is always finitely generated (i.e., there always exists a finite set of group generators). This theorem ...

A number n is said to be divisible by d if d is a divisor of n. The function Divisible[n, d] returns True if an integer n is divisible by an integer d. The product of any n ...

The Golomb graph is a unit-distance graph discovered around 1960-1965 by Golomb (Soifer 2008, p. 19). It is implemented in the Wolfram Language as GraphData["GolombGraph"]. A ...

Schur's partition theorem lets A(n) denote the number of partitions of n into parts congruent to +/-1 (mod 6), B(n) denote the number of partitions of n into distinct parts ...

A k-matching in a graph G is a set of k edges, no two of which have a vertex in common (i.e., an independent edge set of size k). Let Phi_k be the number of k-matchings in ...

A prime which does not divide the class number h(p) of the cyclotomic field obtained by adjoining a primitive pth root of unity to the field of rationals. A prime p is ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

In combinatorial mathematics, the series-parallel networks problem asks for the number of networks that can be formed using a given number of edges. The edges can be ...

The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x (Shanks 1993, p. 15). For example, there are no primes ...

The Kaprekar routine is an algorithm discovered in 1949 by D. R. Kaprekar for 4-digit numbers, but which can be generalized to k-digit numbers. To apply the Kaprekar routine ...