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The partial differential equation u_(tt)-u_(xx)-u+u^3=0.

The partial differential equation u_(tt)-u_(xx)=epsilon(u_t-u_t^3).

The partial differential equation u_t+u_x-6uu_x-u_(txx)=0.

The partial differential equation u_(yy)=yu_(xx).

If a fixed fraction x of a given amount of money P is lost, and then the same fraction x of the remaining amount is gained, the result is less than the original and equal to ...

The Benney equation in 1+1 dimensions is the nonlinear partial differential equation ...

For a simple continued fraction x=[a_0,a_1,...] with convergents p_n/q_n, the fundamental recurrence relation is given by p_nq_(n-1)-p_(n-1)q_n=(-1)^(n+1).

A unit fraction is a fraction with numerator 1. Examples of unit fractions include 1/2, 1/3, 1/12, and 1/123456. The famous Rhind papyrus, dated to around 1650 BC, discusses ...

The continued fraction ((x+1)^n-(x-1)^n)/((x+1)^n+(x-1)^n)=n/(x+)(n^2-1)/(3x+)(n^2-2^2)/(5x+...).

Every irrational number x can be expanded in a unique continued fraction expansion x=b_0+(e_1)/(b_1+(e_2)/(b_2+(e_3)/(b_3+...)))=[b_0;e_1b_1,e_2b_2,e_3b_3,...] such that b_0 ...