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There are at least two statements which go by the name of Artin's conjecture. If r is any complex finite-dimensional representation of the absolute Galois group of a number ...

An infinite sequence of positive integers 1<=b_1<b_2<b_3<..., (1) also called a Sidon sequence, such that all pairwise sums b_i+b_j (2) for i<=j are distinct (Guy 1994). An ...

Let E_n(f) be the error of the best uniform approximation to a real function f(x) on the interval [-1,1] by real polynomials of degree at most n. If alpha(x)=|x|, (1) then ...

The biggest little polygon with n sides is the convex plane n-gon of unit polygon diameter having largest possible area. Reinhardt (1922) showed that for n odd, the regular ...

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

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 ...

Let F be the set of complex analytic functions f defined on an open region containing the set closure of the unit disk D={z:|z|<1} satisfying f(0)=0 and df/dz(0)=1. For each ...

A two-dimensional binary (k=2) totalistic cellular automaton with a von Neumann neighborhood of range r=1. It has a birth rule that at least 2 of its 4 neighbors are alive, ...

Borsuk conjectured that it is possible to cut an n-dimensional shape of generalized diameter 1 into n+1 pieces each with diameter smaller than the original. It is true for ...

The Cantor function F(x) is the continuous but not absolutely continuous function on [0,1] which may be defined as follows. First, express x in ternary. If the resulting ...