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A fraction a/b written in lowest terms, i.e., by dividing numerator and denominator through by their greatest common divisor (a,b). For example, 2/3 is the reduced fraction ...

The simple continued fraction representations of e given by [2; 1, 2, 1, 1, 4, 1, 1, 6, ...] (OEIS A003417). This continued fraction is sometimes known as Euler's continued ...

A rational number expressed in the form a/b (in-line notation) or a/b (traditional "display" notation), where a is called the numerator and b is called the denominator. When ...

An algorithm for computing an Egyptian fraction, called the Farey sequence method by Bleicher (1972).

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^').

An algorithm for computing an Egyptian fraction (Stewart 1992).

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

A reducible fraction is a fraction p/q such that GCD(p,q)>1, i.e., p/q can be written in reduced form. A fraction that is not reducible is said to be irreducible. For ...

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 ...

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 ...