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Find a square number x^2 such that, when a given integer h is added or subtracted, new square numbers are obtained so that x^2+h=a^2 (1) and x^2-h=b^2. (2) This problem was ...

Fermat's 4n+1 theorem, sometimes called Fermat's two-square theorem or simply "Fermat's theorem," states that a prime number p can be represented in an essentially unique ...

A closed planar quadrilateral with opposite sides of equal lengths a and b, and with four right angles. A square is a degenerate rectangle with a=b. The area of the rectangle ...

A cograph (or "complement-reducible graph") is simple graph defined by the criteria 1. K_1 is a cograph, 2. If X is a cograph, then so is its graph complement, and 3. If X ...

A 24-dimensional Euclidean lattice. An automorphism of the Leech lattice modulo a center of two leads to the Conway group Co_1. Stabilization of the one- and two-dimensional ...

Ramanujan's two-variable theta function f(a,b) is defined by f(a,b)=sum_(n=-infty)^inftya^(n(n+1)/2)b^(n(n-1)/2) (1) for |ab|<1 (Berndt 1985, p. 34; Berndt et al. 2000). It ...

A special function is a function (usually named after an early investigator of its properties) having a particular use in mathematical physics or some other branch of ...

By analogy with the sinc function, define the tanc function by tanc(z)={(tanz)/z for z!=0; 1 for z=0. (1) Since tanz/z is not a cardinal function, the "analogy" with the sinc ...

An algorithm which finds a polynomial recurrence for terminating hypergeometric identities of the form sum_(k)(n; ...

The q-binomial coefficient is a q-analog for the binomial coefficient, also called a Gaussian coefficient or a Gaussian polynomial. A q-binomial coefficient is given by [n; ...