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Given a Farey sequence with consecutive terms h/k and h^'/k^', then the mediant is defined as the reduced form of the fraction (h+h^')/(k+k^').

A method for computing an Egyptian fraction. This method always terminates (Beeckmans 1993).

Apéry's constant is defined by zeta(3)=1.2020569..., (1) (OEIS A002117) where zeta(z) is the Riemann zeta function. Apéry (1979) proved that zeta(3) is irrational, although ...

Lagrange's continued fraction theorem, proved by Lagrange in 1770, states that any positive quadratic surd sqrt(a) has a regular continued fraction which is periodic after ...

The nth partial numerator in a generalized continued fraction b_0+K_(n=1)^infty(a_n)/(b_n) is the expression a_n. For a simple continued fraction b_0+K_(n=1)^infty1/(b_n), ...

A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of ...

A simple continued fraction is a special case of a generalized continued fraction for which the partial numerators are equal to unity, i.e., a_n=1 for all n=1, 2, .... A ...

Consider the problem of comparing two real numbers x and y based on their continued fraction representations. Then the mean number of iterations needed to determine if x<y or ...

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 ...

A Lehner continued fraction is a generalized continued fraction of the form b_0+(e_1)/(b_1+(e_2)/(b_2+(e_3)/(b_3+...))) where (b_i,e_(i+1))=(1,1) or (2, -1) for x in [1,2) an ...