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The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

Apéry's constant is defined by zeta(3)=1.2020569..., (1) (OEIS A002117) where zeta(z) is the Riemann zeta function. Apéry (1979) proved that zeta(3) is irrational, although ...

A harmonic number is a number of the form H_n=sum_(k=1)^n1/k (1) arising from truncation of the harmonic series. A harmonic number can be expressed analytically as ...

The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...

A problem is an exercise whose solution is desired. Mathematical "problems" may therefore range from simple puzzles to examination and contest problems to propositions whose ...

Zeros of the Riemann zeta function zeta(s) come in two different types. So-called "trivial zeros" occur at all negative even integers s=-2, -4, -6, ..., and "nontrivial ...

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides ...

The constant e is base of the natural logarithm. e is sometimes known as Napier's constant, although its symbol (e) honors Euler. e is the unique number with the property ...

Let P be a finite partially ordered set, then an antichain in P is a set of pairwise incomparable elements. Antichains are also called Sperner systems in older literature ...