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A polygonal number and 6-polygonal number of the form n(2n-1). The first few are 1, 6, 15, 28, 45, ... (OEIS A000384). The generating function for the hexagonal numbers is ...

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 ...

A trinomial coefficient is a coefficient of the trinomial triangle. Following the notation of Andrews (1990), the trinomial coefficient (n; k)_2, with n>=0 and -n<=k<=n, is ...

Elder's theorem is a generalization of Stanley's theorem which states that the total number of occurrences of an integer k among all unordered partitions of n is equal to the ...

Let there be n ways for a "good" selection and m ways for a "bad" selection out of a total of n+m possibilities. Take N samples and let x_i equal 1 if selection i is ...

The Wagner graph is a name sometimes given to the 4-Möbius ladder (Bondy and Murty 2008, pp. 275-276). The association arises through the theorem of Wagner (1937) that graphs ...

An amicable pair (m,n) consists of two integers m,n for which the sum of proper divisors (the divisors excluding the number itself) of one number equals the other. Amicable ...

17 is a Fermat prime, which means that the 17-sided regular polygon (the heptadecagon) is constructible using compass and straightedge (as proved by Gauss).

A nonreflexible regular map of genus 7 with eight graph vertices, 28 graph edges, and eight heptagonal faces.

A point p on a regular surface M in R^3 is said to be elliptic if the Gaussian curvature K(p)>0 or equivalently, the principal curvatures kappa_1 and kappa_2 have the same ...