Mga halimbawa ng paggamit ng Euclidean algorithm sa Ingles at ang kanilang mga pagsasalin sa Tagalog
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The following year he wrote on number theory,making a contribution to the theory of the Euclidean algorithm.
The method here is essentially the use of the Euclidean algorithm to find the highest common factor of a and b but is also related to continued fractions.
One of the first papers which he published after arriving in the United States was on the Euclidean algorithm in principal ideal domains.
While at Bristol he worked on the Euclidean algorithm(norm function)in a general setting having already proved while at Cambridge that there are only finitely many real quadratic fields with a Euclidean algorithm.
In particular book seven is a self-contained introduction to number theory and contains the Euclidean algorithm for finding the greatest common divisor of two numbers.
In 1733 de Lagny examined the continued fraction expansion of the quotient of two integers and, as an example,considered adjacent Fibonacci numbers as the worst case expansion for the Euclidean algorithm.
In lighter moments he may turn to the theory ofthe game of Nim, while on more austere occasions he may study the question of Euclidean algorithms in algebraic fields, or the Rogers-Ramanujan identities in the theory of partitions.
The proof is very typical of Motzkin in that the Euclidean algorithm is given a new formulation, which at first seems to be leading away from the problem at hand, but is suddenly seen to be the decisive key to its solution.
He also did important work on differential geometry and, in another contribution to number theory,he showed that the number of divisions in the Euclidean algorithm never exceeds five times the number of digits in the smaller number.