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A flexagon made by folding a strip into adjacent equilateral triangles. The number of states possible in a hexaflexagon is the Catalan number C_5=42.

A spectrum containing the real numbers larger than Freiman's constant.

Minimal surfaces are defined as surfaces with zero mean curvature. A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange's equation, ...

Let E be an elliptic curve defined over the field of rationals Q(sqrt(-d)) having equation y^2=x^3+ax+b with a and b integers. Let P be a point on E with integer coordinates ...

There are two kinds of Bell polynomials. A Bell polynomial B_n(x), also called an exponential polynomial and denoted phi_n(x) (Bell 1934, Roman 1984, pp. 63-67) is a ...

There are a number of functions in various branches of mathematics known as Riemann functions. Examples include the Riemann P-series, Riemann-Siegel functions, Riemann theta ...

A generalization of Fermat's last theorem which states that if a^x+b^y=c^z, where a, b, c, x, y, and z are any positive integers with x,y,z>2, then a, b, and c have a common ...

A triple (a,b,c) of positive integers satisfying a<b<c is said to be geometric if ac=b^2. In particular, such a triple is geometric if its terms form a geometric sequence ...

The number 10 (ten) is the basis for the decimal system of notation. In this system, each "decimal place" consists of a digit 0-9 arranged such that each digit is multiplied ...

Lucas's theorem states that if n>=3 be a squarefree integer and Phi_n(z) a cyclotomic polynomial, then Phi_n(z)=U_n^2(z)-(-1)^((n-1)/2)nzV_n^2(z), (1) where U_n(z) and V_n(z) ...