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Arnauld's paradox states that if negative numbers exist, then (-1)/1 must equal 1/(-1), which asserts that the ratio of a smaller to a larger quantity equals the ratio of the ...

The sequence whose definition is: "t is the first, fourth, eleventh, ... letter of this sentence." The first few values are 1, 4, 11, 16, 24, 29, 33, 35, 39, ... (OEIS ...

An Artin L-function over the rationals Q encodes in a generating function information about how an irreducible monic polynomial over Z factors when reduced modulo each prime. ...

A general reciprocity theorem for all orders which covered all other known reciprocity theorems when proved by E. Artin in 1927. If R is a number field and R^' a finite ...

A series is called artistic if every three consecutive terms have a common three-way ratio P[a_i,a_(i+1),a_(i+2)]=((a_i+a_(i+1)+a_(i+2))a_(i+1))/(a_ia_(i+2)). A series is ...

A sequence {x_n} is called an infinitive sequence if, for every i, x_n=i for infinitely many n. Write a(i,j) for the jth index n for which x_n=i. Then as i and j range ...

The group of functions from an object G to itself which preserve the structure of the object, denoted Aut(G). The automorphism group of a group preserves the multiplication ...

The average disorder number of a simple connected graph on n vertices is defined as the average length of a walk along the edges of the graph taken over all ordering of its ...

The baby monster group, also known as Fischer's baby monster group, is the second-largest sporadic group. It is denoted B and has group order |B| = ...

Ballantine's series is the series for pi given by pi=864sum_(n=0)^infty((n!)^24^n)/((2n+1)!325^(n+1)) +1824sum_(n=0)^infty((n!)^24^n)/((2n+1)!3250^(n+1))-20cot^(-1)239 ...