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Any prime number other than 2 (which is the unique even prime). Humorously, 2 is therefore the "oddest" prime.

The sequence composed of 1s and 2s obtained by starting with the number 1, and picking subsequent elements to avoid repeating the longest possible substring. The first few ...

An ordered factorization is a factorization (not necessarily into prime factors) in which a×b is considered distinct from b×a. The following table lists the ordered ...

Given two circles, draw the tangents from the center of each circle to the sides of the other. Then the line segments AB and CD are of equal length. The theorem can be proved ...

(x^2)/(a^2-lambda)+(y^2)/(b^2-lambda)=z-lambda (1) (x^2)/(a^2-mu)+(y^2)/(b^2-mu)=z-mu (2) (x^2)/(a^2-nu)+(y^2)/(b^2-nu)=z-nu, (3) where lambda in (-infty,b^2), mu in ...

The ordinary differential equation y^('')+r/zy^'=(Az^m+s/(z^2))y. (1) It has solution y=c_1I_(-nu)((2sqrt(A)z^(m/2+1))/(m+2))z^((1-r)/2) ...

An element of order 2 in a group (i.e., an element A of a group such that A^2=I, where I is the identity element).

Two numbers are homogeneous if they have identical prime factors. An example of a homogeneous pair is (6, 72), both of which share prime factors 2 and 3: 6 = 2·3 (1) 72 = ...

A number which can be represented both in the form x_0^2-Dy_0^2 and in the form Dx_1^2-y_1^2. This is only possible when the Pell equation x^2-Dy^2=-1 (1) is solvable. Then ...

Consider the family of ellipses (x^2)/(c^2)+(y^2)/((1-c)^2)-1=0 (1) for c in [0,1]. The partial derivative with respect to c is -(2x^2)/(c^3)+(2y^2)/((1-c)^3)=0 (2) ...