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An amicable quadruple as a quadruple (a,b,c,d) such that sigma(a)=sigma(b)=sigma(c)=sigma(d)=a+b+c+d, (1) where sigma(n) is the divisor function. If (a,b) and (x,y) are ...

Dickson (1913, 2005) defined an amicable triple to be a triple of three numbers (l,m,n) such that s(l) = m+n (1) s(m) = l+n (2) s(n) = l+m, (3) where s(n) is the restricted ...

Two points which are collinear with respect to a similitude center but are not homologous points. Four interesting theorems from Johnson (1929) follow. 1. Two pairs of ...

Any square matrix A can be written as a sum A=A_S+A_A, (1) where A_S=1/2(A+A^(T)) (2) is a symmetric matrix known as the symmetric part of A and A_A=1/2(A-A^(T)) (3) is an ...

An Appell sequence is a Sheffer sequence for (g(t),t). Roman (1984, pp. 86-106) summarizes properties of Appell sequences and gives a number of specific examples. The ...

"Arabic numerals" are the numerical symbols 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. Historically, Indian numerals evolved in Arab usage roughly 1000 A.D., and there was rare ...

The surface which is the inverse of the ellipsoid in the sense that it "goes in" where the ellipsoid "goes out." It is given by the parametric equations x = acos^3ucos^3v (1) ...

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 ...

The axiom of Zermelo-Fraenkel set theory which asserts the existence of a set containing all the natural numbers, exists x(emptyset in x ^ forall y in x(y^' in x)), where ...

A 1-variable unoriented knot polynomial Q(x). It satisfies Q_(unknot)=1 (1) and the skein relationship Q_(L_+)+Q_(L_-)=x(Q_(L_0)+Q_(L_infty)). (2) It also satisfies ...