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Continued fraction. A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this ...
The gamma function is an important special function in mathematics. Its particular values can be expressed in closed form for integer and half-integer arguments, but no simple expressions are known for the values at rational points in general. Other fractional arguments can be approximated through efficient infinite products, infinite series ...
An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). [1] In other words, a fraction a b is irreducible if and only if a and b are coprime, that is ...
Generalization to fractions is by multiplying the numerators and denominators, respectively: = (). This gives the area of a rectangle A B {\displaystyle {\frac {A}{B}}} high and C D {\displaystyle {\frac {C}{D}}} wide, and is the same as the number of things in an array when the rational numbers happen to be whole numbers.
In mathematics, the greatest common divisor (GCD), also known as greatest common factor (GCF), of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted . For example, the GCD of 8 and 12 is 4, that is, gcd (8, 12 ...
Approximating an irrational number by a fraction π: 22/7 1-digit-denominator Approximating a rational number by a fraction with smaller denominator 399 / 941 3 / 7 1-digit-denominator Approximating a fraction by a fractional decimal number: 5 / 3 1.6667: 4 decimal places: Approximating a fractional decimal number by one with fewer digits 2.1784
Let Δ be a negative integer with Δ = −dn, where d is a multiplier and Δ is the negative discriminant of some quadratic form. Take the t first primes p 1 = 2, p 2 = 3, p 3 = 5, ..., p t, for some t ∈ N. Let f q be a random prime form of G Δ with ( Δ / q ) = 1. Find a generating set X of G Δ.
It can be used to reduce fractions to their simplest form, and is a part of many other number-theoretic and cryptographic calculations. The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number.