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A very general theorem that allows the number of discrete combinatorial objects of a given type to be enumerated (counted) as a function of their "order." The most common ...

A proof that is only based on visual elements, without any comments. An arithmetic identity can be demonstrated by a picture showing a self-evident equality between numerical ...

For any constructible function f, there exists a function P_f such that for all functions t, the following two statements are equivalent: 1. There exists an algorithm A such ...

Let G be a finite, connected, undirected graph with graph diameter d(G) and graph distance d(u,v) between vertices u and v. A radio labeling of a graph G is labeling using ...

Rational numbers are countable, so an order can be placed on them just like the natural numbers. Although such an ordering is not obvious (nor unique), one such ordering can ...

There are at least two Siegel's theorems. The first states that an elliptic curve can have only a finite number of points with integer coordinates. The second states that if ...

The nth Smarandache-Wellin number is formed from the consecutive number sequence obtained by concatenating of the digits of the first n primes. The first few are 2, 23, 235, ...

A Stoneham number is a number alpha_(b,c) of the form alpha_(b,c)=sum_(k=1)^infty1/(b^(c^k)c^k), where b,c>1 are relatively prime positive integers. Stoneham (1973) proved ...

Let T(x,y,z) be the number of times "otherwise" is called in the TAK function, then the Takeuchi numbers are defined by T_n(n,0,n+1). A recursive formula for T_n is given by ...

A Thâbit ibn Kurrah number, sometimes called a 321-number, is a number of the form K_n=3·2^n-1. The first few for n=0, 1, ... are 2, 5, 11, 23, 47, 95, 191, 383, 767, ... ...