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The Gelfond-Schneider constant is sometimes known as the Hilbert number. Flannery and Flannery (2000, p. 35) define a Hilbert number as a positive integer of the form n=4k+1 ...

If all the diagonals--including those obtained by "wrapping around" the edges--of a magic square sum to the same magic constant, the square is said to be a panmagic square ...

Any entire analytic function whose range omits two points must be a constant function. Of course, an entire function that omits a single point from its range need not be a ...

A fundamental structural result in extremal graph theory due to Szemerédi (1978). The regularity lemma essentially says that every graph can be well-approximated by the union ...

A function f(x) is said to be antiperiodic with antiperiod p if -f(x)=f(x+np) for n=1, 3, .... For example, the sine function sinx is antiperiodic with period pi (as well as ...

There are (at least) two mathematical objects known as Weierstrass forms. The first is a general form into which an elliptic curve over any field K can be transformed, given ...

In his monumental treatise Disquisitiones Arithmeticae, Gauss conjectured that the class number h(-d) of an imaginary quadratic field with binary quadratic form discriminant ...

A valuation for which |x|<=1 implies |1+x|<=C for the constant C=1 (independent of x). Such a valuation does not satisfy the strong triangle inequality |x+y|<=max(|x|,|y|).

The geodesics on a general cylinder generated by lines parallel to a line l with which the tangent makes a constant angle.

n sets of s trials each, with the probability of success p constant in each set. var(x/n)=spq+s(s-1)sigma_p^2, where sigma_p^2 is the variance of p_i.