- #1
MienTommy
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In this video, at 5:35 He has d/(a-qb) for the first part. I was not sure how he got that. Why is it not d/(a+qb)?
Because d/a and d/bc implies d/(a+bc)
Why does +bc become negative?
The Euclidian Algorithm is a mathematical method for finding the greatest common divisor (GCD) of two numbers. It is based on the principle that the GCD of two numbers is equal to the GCD of the smaller number and the remainder of the larger number divided by the smaller number.
The Euclidian Algorithm is important because it is the most efficient method for finding the GCD of two numbers. It is also used in various other mathematical calculations, such as finding the least common multiple and solving linear Diophantine equations.
The Euclidian Algorithm can be proved using the principle of mathematical induction. The base case is when the smaller number is equal to 0, in which case the GCD is the larger number. For the inductive step, it is assumed that the algorithm works for two numbers, and then it is shown that it also works for the next set of numbers using the remainder and the smaller number.
Yes, the Euclidian Algorithm can be extended to find the GCD of multiple numbers. This is done by finding the GCD of the first two numbers, and then using that GCD and the third number to find the GCD of all three numbers, and so on until all numbers have been considered.
Yes, the Euclidian Algorithm can be used for any type of numbers that can be divided and have a remainder. This includes rational numbers and even complex numbers. The same principle of finding the GCD of the smaller number and the remainder of the larger number divided by the smaller number applies in these cases as well.