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If r is a root of a nonzero polynomial equation a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, (1) where the a_is are integers (or equivalently, rational numbers) and r satisfies no ...

The Burnside problem originated with Burnside (1902), who wrote, "A still undecided point in the theory of discontinuous groups is whether the group order of a group may be ...

The conjugate gradient method is an algorithm for finding the nearest local minimum of a function of n variables which presupposes that the gradient of the function can be ...

A derangement is a permutation in which none of the objects appear in their "natural" (i.e., ordered) place. For example, the only derangements of {1,2,3} are {2,3,1} and ...

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 ...

A magic tesseract is a four-dimensional generalization of the two-dimensional magic square and the three-dimensional magic cube. A magic tesseract has magic constant ...

Q(n), also denoted q(n) (Abramowitz and Stegun 1972, p. 825), gives the number of ways of writing the integer n as a sum of positive integers without regard to order with the ...

A polygonal number is a type of figurate number that is a generalization of triangular, square, etc., to an n-gon for n an arbitrary positive integer. The above diagrams ...

A primality test is a test to determine whether or not a given number is prime, as opposed to actually decomposing the number into its constituent prime factors (which is ...

Rule 30 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...