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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 ...

Every even number is the difference of two consecutive primes in infinitely many ways (Dickson 2005, p. 424). If true, taking the difference 2, this conjecture implies that ...

The chromatic polynomial pi_G(z) of an undirected graph G, also denoted C(G;z) (Biggs 1973, p. 106) and P(G,x) (Godsil and Royle 2001, p. 358), is a polynomial which encodes ...

A simple graph, also called a strict graph (Tutte 1998, p. 2), is an unweighted, undirected graph containing no graph loops or multiple edges (Gibbons 1985, p. 2; West 2000, ...

Schur (1916) proved that no matter how the set of positive integers less than or equal to |_n!e_| (where |_x_| is the floor function) is partitioned into n classes, one class ...

For F_n the nth Fibonacci number, F_(n-1)F_(n+1)-F_n^2=(-1)^n. This identity was also discovered by Simson (Coxeter and Greitzer 1967, p. 41; Coxeter 1969, pp. 165-168; Wells ...

A method for generating random (pseudorandom) numbers using the linear recurrence relation X_(n+1)=aX_n+c (mod m), where a and c must assume certain fixed values, m is some ...

The process of approximating a quantity, be it for convenience or, as in the case of numerical computations, of necessity. If rounding is performed on each of a series of ...

Let the minimal length of an addition chain for a number n be denoted l(n). Then the Scholz conjecture, also called the Scholz-Brauer conjecture or Brauer-Scholz conjecture, ...

A class of knots containing the class of alternating knots. Let c(K) be the link crossing number. Then for knot sum K_1#K_2 which is an adequate knot, ...