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Let s_1, s_2, ... be an infinite series of real numbers lying between 0 and 1. Then corresponding to any arbitrarily large K, there exists a positive integer n and two ...

If an infinite number of points in the plane are all separated by integer distances, then all the points lie on a straight line.

An Euler brick is a cuboid that possesses integer edges a>b>c and face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2). (3) If the ...

A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an ...

An idoneal number, also called a suitable number or convenient number, is a positive integer D for which the fact that a number is a monomorph (i.e., is expressible in only ...

The orthogonal decomposition of a matrix into lower trapezoidal matrices.

The Legendre differential equation is the second-order ordinary differential equation (1-x^2)(d^2y)/(dx^2)-2x(dy)/(dx)+l(l+1)y=0, (1) which can be rewritten ...

Macdonald's plane partition conjecture proposes a formula for the number of cyclically symmetric plane partitions (CSPPs) of a given integer whose Ferrers diagrams fit inside ...

An element B of a ring is nilpotent if there exists a positive integer k for which B^k=0.

A sieving procedure that can be used in conjunction with Dixon's factorization method to factor large numbers n. Pick values of r given by r=|_sqrt(n)_|+k, (1) where k=1, 2, ...