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Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

A minimal cover is a cover for which removal of any single member destroys the covering property. For example, of the five covers of {1,2}, namely {{1},{2}}, {{1,2}}, ...

The modular equation of degree n gives an algebraic connection of the form (K^'(l))/(K(l))=n(K^'(k))/(K(k)) (1) between the transcendental complete elliptic integrals of the ...

A sequence of positive integers 1<=a_1<a_2<a_3<... (1) is a nonaveraging sequence if it contains no three terms which are in an arithmetic progression, i.e., terms such that ...

A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2), (3) and an ...

The sequence {|_(3/2)^n_|} is given by 1, 1, 2, 3, 5, 7, 11, 17, 25, 38, ... (OEIS A002379). The first few composite |_(3/2)^n_| occur for n=8, 9, 10, 11, 12, 13, 14, 15, 16, ...

A rational amicable pair consists of two integers a and b for which the divisor functions are equal and are of the form sigma(a)=sigma(b)=(P(a,b))/(Q(a,b))=R(a,b), (1) where ...

The rational distance problem asks to find a geometric configuration satisfying given properties such that all distances along specific edges are rational numbers. (This is ...

A polyhedron is said to be regular if its faces and vertex figures are regular (not necessarily convex) polygons (Coxeter 1973, p. 16). Using this definition, there are a ...

Self-recursion is a recursion that is defined in terms of itself, resulting in an ill-defined infinite regress. The formula for the volume of a cylinder leads to the ...