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The number of alternating permutations for n elements is sometimes called an Euler zigzag number. Denote the number of alternating permutations on n elements for which the ...

Define g(k) as the quantity appearing in Waring's problem, then Euler conjectured that g(k)=2^k+|_(3/2)^k_|-2, where |_x_| is the floor function.

The problem of finding in how many ways E_n a plane convex polygon of n sides can be divided into triangles by diagonals. Euler first proposed it to Christian Goldbach in ...

A graph vertex in a graph is said to be an even node if its vertex degree is even.

10^(18) bytes. Unfortunately, the term is sometimes also used to mean 2^(60)=1024^6 bytes. However, the latter usage is deprecated, and the term exbibyte is preferred for ...

2^(60)=1024^6 bytes. Although the term exabyte is sometimes used to refer to 1024^6 bytes, such usage is deprecated in favor of the standard SI naming convention of 1 exabyte ...

A binomial coefficient (N; k) is said to be exceptional if lpf(N; k)>N/k. The following table gives the exception binomial coefficients which are also good binomial ...

A disjunction that is true if only one, but not both, of its arguments are true, and is false if neither or both are true, which is equivalent to the XOR connective. By ...

For discrete problems in which no efficient solution method is known, it might be necessary to test each possibility sequentially in order to determine if it is the solution. ...

If at least one solution can be determined for a given problem, a solution to that problem is said to exist. Frequently, mathematicians seek to prove the existence of ...