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An Egyptian fraction is the sum of a finite number of reciprocals of positive integers. According to the proof of the Erdős–Graham problem, if the set of integers greater than one is partitioned into finitely many subsets, then one of the subsets can be used to form an Egyptian fraction representation of 1.
Fibonacci provides tables of these representations for fractions having as denominators the practical numbers 6, 8, 12, 20, 24, 60, and 100. Vose (1985) showed that every rational number / has an Egyptian fraction representation with () terms.
For example, the content of + may be either 2 or −2, since 2 is the greatest common divisor of −12, 30, and −20. If one chooses 2 as the content, the primitive part of this polynomial is If one chooses 2 as the content, the primitive part of this polynomial is
Although it is not a book on fractions, the meaning, nature, and four operations of fractions are fully discussed. For example: combined division (addition), subtraction (subtraction), multiplication (multiplication), warp division (division), division (comparison size), reduction (simplified fraction), and bisector (average). [9]
In the analytic theory of continued fractions, Euler's continued fraction formula is an identity connecting a certain very general infinite series with an infinite continued fraction. First published in 1748, it was at first regarded as a simple identity connecting a finite sum with a finite continued fraction in such a way that the extension ...
A ham sandwich. The ham sandwich theorem takes its name from the case when n = 3 and the three objects to be bisected are the ingredients of a ham sandwich.Sources differ on whether these three ingredients are two slices of bread and a piece of ham (Peters 1981), bread and cheese and ham (Cairns 1963), or bread and butter and ham (Dubins & Spanier 1961).
In combinatorial optimization, the matroid parity problem is a problem of finding the largest independent set of paired elements in a matroid. [1] The problem was formulated by Lawler (1976) as a common generalization of graph matching and matroid intersection. [1] [2] It is also known as polymatroid matching, or the matchoid problem. [3]
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