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If a, b, c, and d are points in the extended complex plane C^*, their cross ratio, also called the cross-ratio (Courant and Robbins 1996, p. 172; Durell 1928, p. 73), ...

The largest cube dividing a positive integer n. For n=1, 2, ..., the first few are 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, ... (OEIS A008834).

A natural number n>3 such that n|(a^(n-2)-a) whenever (a,n)=1 (a and n are relatively prime) and a<=n. (Here, n|m means that n divides m.) There are an infinite number of ...

A figurate number of the form 4n^2-3n. The first few are 1, 10, 27, 52, 85, ... (OEIS A001107). The generating function giving the decagonal numbers is ...

An even number N for which N=0 (mod 4). The first few positive doubly even numbers are 4, 8, 12, 16, ... (OEIS A008586).

A proof which can be accomplished using only real numbers (i.e., real analysis instead of complex analysis; Hoffman 1998, pp. 92-93).

An equation is a mathematical expression stating that two or more quantities are the same as one another, also called an equality, formula, or identity.

An Euler pseudoprime to the base b is a composite number n which satisfies b^((n-1)/2)=+/-1 (mod n). The first few base-2 Euler pseudoprimes are 341, 561, 1105, 1729, 1905, ...

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(a,n)=1/aint_0^infty[1-e^(aEi(-t))sum_(k=0)^(n-1)((-a)^k[Ei(-t)]^k)/(k!)]. Then the Flajolet-Odlyzko constant is defined as G(1/2,1)=0.757823011268... (OEIS A143297).