Euclidean algorithm - Wikipedia
In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for For example, 21 is the GCD of and (as = 21 × 12 and = 21 × 5), Synonyms for the GCD include the greatest common factor (GCF ), the than 1 divides both 6 and 35, since they have no prime factors in common . Christian Rudder: The dating site's numbers guru reveals the painful Reading from the top, we see that 20 and year-old women prefer. Applications in the Environmental Sciences E.R. Cook, L.A. Kairiukstis. Aniol Growth Losses in Norway Spruce Stands Caused by Environmental Factors. Environmental Pollution, Series B 2: Tree-Ring Dating and Archaeology .
The algorithm was probably not discovered by Euclidwho compiled results from earlier mathematicians in his Elements. In the late 5th century, the Indian mathematician and astronomer Aryabhata described the algorithm as the "pulverizer",  perhaps because of its effectiveness in solving Diophantine equations.
The extended Euclidean algorithm was published by the English mathematician Nicholas Saunderson who attributed it to Roger Cotes as a method for computing continued fractions efficiently.
What integers have been factored with Shor's algorithm? - Quantum Computing Stack Exchange
InCarl Gauss used the Euclidean algorithm to demonstrate unique factorization of Gaussian integersalthough his work was first published in For example, Dedekind was the first to prove Fermat's two-square theorem using the unique factorization of Gaussian integers. In the closing decades of the 19th century, the Euclidean algorithm gradually became eclipsed by Dedekind's more general theory of ideals.
Seminumerical Algorithms, 2nd editionp. Other applications of Euclid's algorithm were developed in the 19th century.
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InCharles Sturm showed that the algorithm was useful in the Sturm chain method for counting the real roots of polynomials in any given interval. Several novel integer relation algorithms have been developed, such as the algorithm of Helaman Ferguson and R.
Forcade  and the LLL algorithm. The players take turns removing m multiples of the smaller pile from the larger. The winner is the first player to reduce one pile to zero stones.Finding all the Factors of a Number
The process of substituting remainders by formulae involving their predecessors can be continued until the original numbers a and b are reached: Some babies with Down syndrome are born with intestinal malformations that require surgery.
Common visual problems include crossed eyes, near- or farsightedness, and cataracts. Most visual problems can be improved with glasses, surgery, or other treatments. A pediatric ophthalmologist should be consulted within the first year of life. All children with Down syndrome should have regular vision and hearing examinations so any problems can be treated before they hinder development of language and other skills.
Children with Down syndrome are at increased risk for thyroid problems and leukemia.
They also tend to have many colds, as well as bronchitis and pneumonia. Children with Down syndrome should receive regular medical care, including childhood immunizations. The National Down Syndrome Congress publishes a "Preventive Medicine Checklist" that outlines which checkups and medical tests are recommended at various ages. How significant is the degree of intellectual disability that accompanies Down syndrome? The degree of intellectual disability that accompanies Down syndrome varies widely.
However, most intellectual disability falls within the mild to moderate range. There is no way to predict the mental development of a child with Down syndrome based on their physical features.
Children with Down syndrome can usually do most things that any young child can do, such as walking, talking, dressing, and being toilet trained. However, they generally do these things later than other children. The exact age that these developmental milestones will be achieved cannot be predicted. However, early intervention programs, beginning in infancy, can help these children achieve their individual potential.
Can a child with Down syndrome go to school? There are special programs beginning in the preschool years to help children with Down syndrome develop skills as fully as possible.
Along with benefiting from early intervention and special education, many children can be integrated into the regular classroom, to some extent. Many will learn to read and write and participate in diverse childhood activities, both at school and in their neighborhoods.
Today, an increasing number of adults with Down syndrome live semi-independently in community group homes. They take care of themselves, participate in household chores, develop friendships, partake in leisure activities, and work in their communities. Can people with Down syndrome marry? Some people with Down syndrome marry. Although there have been rare exceptions, most men with Down syndrome cannot father a child. How is Down syndrome diagnosed? Since Down syndrome has such a unique group of characteristics, physicians can sometimes determine whether a baby has Down syndrome simply by physical examination.
This information is important in determining the risk in future pregnancies. Translocation Down syndrome and mosaic Down syndrome have different recurrence risks in future pregnancies. Chromosomal abnormalities such as Down syndrome can often be diagnosed before birth by analyzing cells in the amniotic fluid or from the placenta.
Fetal ultrasound during pregnancy can also give information about the possibility of Down syndrome, but ultrasound is not percent accurate. Many babies with Down syndrome may look the same on ultrasound as those without Down syndrome.
A chromosome analysis, whether performed on a blood sample, cells from the amniotic fluid, or placenta, is very accurate. What are the maternal age risks for Down syndrome?