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The (associated) Legendre function of the first kind P_n^m(z) is the solution to the Legendre differential equation which is regular at the origin. For m,n integers and z ...

A conjecture concerning primes.

A Sierpiński number of the second kind is a number k satisfying Sierpiński's composite number theorem, i.e., a Proth number k such that k·2^n+1 is composite for every n>=1. ...

In Book IX of The Elements, Euclid gave a method for constructing perfect numbers (Dickson 2005, p. 3), although this method applies only to even perfect numbers. In a 1638 ...

A monomial is a product of positive integer powers of a fixed set of variables (possibly) together with a coefficient, e.g., x, 3xy^2, or -2x^2y^3z. A monomial can also be ...

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...

The regular polygon of 17 sides is called the heptadecagon, or sometimes the heptakaidecagon. Gauss proved in 1796 (when he was 19 years old) that the heptadecagon is ...

An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor ...

Bowling, known as "ten pins" throughout most of the world, is a game played by rolling a heavy ball down a long narrow track and attempting to knock down ten pins arranged in ...

A binary tree is a tree-like structure that is rooted and in which each vertex has at most two children and each child of a vertex is designated as its left or right child ...