mrashrafkotkaat

25.02.2020 • 

Mathematics

The Euclidean algorithm, which is used to find the greatest common divisor of two non-zero integers, is essentially several applications of the division algorithm. The key arithmetic observation that makes the division algorithm so helpful is the following: If a, b E Z are non-zero and we use the division algorithm to write a = bq+r, for some q,rez, then ged(a, b) = ged(b,r). In class, we brazenly used this fact without proof. It is time to prove that this is always true.(a) Assume that a = bq + r. Let D(a, b) be the set of common divisors of a and b, and let D(br) be the set of common divisors of b and r. Show that D(a, b) = D(0,r). Note that you are asked to show that two sets are equal. Thus, you must show that if D(a,b) C D(b,r) and D(0,r) C D(a,b). (b) Use your result from (a) to conclude that ged(a,b) = ged(b,r).

Ответ:

Kinglilray998

29.12.2021

Mathematics

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Solution: We are given data points and associated residuals:

Data Point           Residual          Absolute value(Residual)

(20,6)                     -2.00                      2.00

(15,5)                       6.75                       6.75

(5,3)                        -1.25                       1.25

(10,10)                     4.50                       4.50

From the above absolute value(Residual) column, we clearly see the data point (15,5) has the residual with greatest absolute value of 6.75.

Therefore, the data point and its associated residual is:

(15,5)  and 6.75    

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