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A theorem, also known as Bachet's conjecture, which Bachet inferred from a lack of a necessary condition being stated by Diophantus. It states that every positive integer can ...

Minkowski's conjecture states that every lattice tiling of R^n by unit hypercubes contains two hypercubes that meet in an (n-1)-dimensional face. Minkowski first considered ...

Modular arithmetic is the arithmetic of congruences, sometimes known informally as "clock arithmetic." In modular arithmetic, numbers "wrap around" upon reaching a given ...

A module is a mathematical object in which things can be added together commutatively by multiplying coefficients and in which most of the rules of manipulating vectors hold. ...

The perspective image of an infinite checkerboard. It can be constructed starting from any triangle DeltaOXY, where OX and OY form the near corner of the floor, and XY is the ...

A quadratic form involving n real variables x_1, x_2, ..., x_n associated with the n×n matrix A=a_(ij) is given by Q(x_1,x_2,...,x_n)=a_(ij)x_ix_j, (1) where Einstein ...

The Siegel theta function is a Gamma_n-invariant meromorphic function on the space of all p×p symmetric complex matrices Z=X+iY with positive definite imaginary part. It is ...

A solitary number is a number which does not have any friends. Solitary numbers include all primes, prime powers, and numbers for which (n,sigma(n))=1, where (a,b) is the ...

There are at least two distinct notions of when a point process is stationary. The most commonly utilized terminology is as follows: Intuitively, a point process X defined on ...

A simplex, sometimes called a hypertetrahedron (Buekenhout and Parker 1998), is the generalization of a tetrahedral region of space to n dimensions. The boundary of a ...