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If the average number of envelopes per pigeonhole is a, then some pigeonhole will have at least a envelopes. Similarly, there must be a pigeonhole with at most a envelopes.

The identity F_n^4-F_(n-2)F_(n-1)F_(n+1)F_(n+2)=1, where F_n is a Fibonacci number.

For any prime number p and any positive integer n, the p^n-rank r_(p^n)(G) of a finitely generated Abelian group G is the number of copies of the cyclic group Z_(p^n) ...

The Hajós number h(G) of a graph G is the maximum k such that G contains a subdivision of the complete graph K_k.

The Hamming distance between two vertices of a hypercube is the number of coordinates at which the two vertices differ.

A matrix is ill-conditioned if the condition number is too large (and singular if it is infinite).

The number of inward directed graph edges from a given graph vertex in a directed graph.

A family of subsets of a topological space such that every point has a neighborhood which intersects only a finite number of them.

A very large number defined in terms of circle notation by Steinhaus (1983) as .

A multiplicative number theoretic function is a number theoretic function f that has the property f(mn)=f(m)f(n) (1) for all pairs of relatively prime positive integers m and ...