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A collection of equations satisfies the Hasse principle if, whenever one of the equations has solutions in R and all the Q_p, then the equations have solutions in the ...

A bishop graph is a graph formed from possible moves of a bishop chess piece, which may make diagonal moves of any length on a chessboard (or any other board). To form the ...

A pentagonal square triangular number is a number that is simultaneously a pentagonal number P_l, a square number S_m, and a triangular number T_n. This requires a solution ...

A biquadratic number is a fourth power, n^4. The first few biquadratic numbers are 1, 16, 81, 256, 625, ... (OEIS A000583). The minimum number of biquadratic numbers needed ...

The word "base" in mathematics is used to refer to a particular mathematical object that is used as a building block. The most common uses are the related concepts of the ...

The rank of a vector bundle is the dimension of its fiber. Equivalently, it is the maximum number of linearly independent local bundle sections in a trivialization. ...

For any Abelian group G and any natural number n, there is a unique space (up to homotopy type) such that all homotopy groups except for the nth are trivial (including the ...

The Diophantine equation sum_(j=1)^(m-1)j^n=m^n. Erdős conjectured that there is no solution to this equation other than the trivial solution 1^1+2^1=3^1, although this ...

A Hermitian metric on a complex vector bundle assigns a Hermitian inner product to every fiber bundle. The basic example is the trivial bundle pi:U×C^k->U, where U is an open ...

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...