Saturday, March 30, 2019

Choosing two numbers a,b, such that the Euclidean algorithm takes 10 steps

The question is to find 2 integers a,b Z for which when applying the Euclidean Algorithm for finding the gcd(a,b) precisely 10 steps are required.
This is what I have done:
Let (a,b) = (427,264)
The 10 steps for the gcd(427,264) are as follows:



427=2641+163



264=1631+101




163=1011+62



101=621+39



62=391+23



39=231+16



23=161+7




16=72+2



7=23+1



2=12+0



I just wanna know if what I have done is right??? or if possible note the place I gone wrong??

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