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The double factorial of a positive integer n is a generalization of the usual factorial n! defined by n!!={n·(n-2)...5·3·1 n>0 odd; n·(n-2)...6·4·2 n>0 even; 1 n=-1,0. (1) ...

The number M_2(n) = 1/nsum_(k=1)^(n^2)k (1) = 1/2n(n^2+1) (2) to which the n numbers in any horizontal, vertical, or main diagonal line must sum in a magic square. The first ...

The Somos sequences are a set of related symmetrical recurrence relations which, surprisingly, always give integers. The Somos sequence of order k, or Somos-k sequence, is ...

A unigraphic graph (or simply a "unigraph") is a graph that is isomorphic to every graph having that degree sequence. All graphs on four are fewer vertices are unigraphic. ...

The unitary divisor function sigma_k^*(n) is the analog of the divisor function sigma_k(n) for unitary divisors and denotes the sum-of-kth-powers-of-the-unitary divisors ...

Assume that n numbered pancakes are stacked, and that a spatula can be used to reverse the order of the top k pancakes for 2<=k<=n. Then the pancake sorting problem asks how ...

The homomorphism S which, according to the snake lemma, permits construction of an exact sequence (1) from the above commutative diagram with exact rows. The homomorphism S ...

A sequence of functions {f_n}, n=1, 2, 3, ... is said to be uniformly convergent to f for a set E of values of x if, for each epsilon>0, an integer N can be found such that ...

The Diophantine equation x_1^2+x_2^2+...+x_n^2=ax_1x_2...x_n which has no integer solutions for a>n.

In response to a letter from Goldbach, Euler considered sums of the form s_h(m,n) = sum_(k=1)^(infty)(1+1/2+...+1/k)^m(k+1)^(-n) (1) = ...