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There exists a positive integer s such that every sufficiently large integer is the sum of at most s primes. It follows that there exists a positive integer s_0>=s such that ...

Consider the circles centered on the midpoints of the sides of a reference triangle and passing though the orthocenter H. These circles cut the sides in six points lying on a ...

Given a Seifert form f(x,y), choose a basis e_1, ..., e_(2g) for H_1(M^^) as a Z-module so every element is uniquely expressible as n_1e_1+...+n_(2g)e_(2g) (1) with n_i ...

A class is a generalized set invented to get around Russell's antinomy while retaining the arbitrary criteria for membership which leads to difficulty for sets. The members ...

Shephard's conjecture states that every convex polyhedron admits a self-unoverlapping unfolding (Shephard 1975). This question is still unsettled (Malkevitch), though most ...

Let the sum of squares function r_k(n) denote the number of representations of n by k squares, then the summatory function of r_2(k)/k has the asymptotic expansion ...

For any M, there exists a t^' such that the sequence n^2+t^', where n=1, 2, ... contains at least M primes.

A knot K in S^3=partialD^4 is a slice knot if it bounds a disk Delta^2 in D^4 which has a tubular neighborhood Delta^2×D^2 whose intersection with S^3 is a tubular ...

A spheroid is an ellipsoid having two axes of equal length, making it a surface of revolution. By convention, the two distinct axis lengths are denoted a and c, and the ...

The average number of regions N(n) into which n lines divide a square is N^_(n)=1/(16)n(n-1)pi+n+1 (Santaló 1976; Finch 2003, p. 481). The maximum number of sequences is ...