Question

6. Euclid's Algorithm, 14pt) In this problem we want to perform Euclid's algorithm, both the basic form, and the extended form. You're welcome to implement it yourself (not taking code from the web, that's cheating), based on the description in the book or in the class to double-check your work, but I strongly suggest that you do this problem by hand, at least once to understand what the steps involved are. a) [5pt] Calculate the gcd of 3848 and 1099 using Euclid's algorithm; show your answer in a 2-column table like the one we saw in class (do not run the extended version for this problem). b) [7pt] Use the extended Euclidean algorithm to calculate the gcd of 607, 47. Show your answer in a 4-column table, the first two columns as before, and the last two columns containing s and t. Hint. you can double-check your values for s and t easily; if you calculate s *607+t*47, in each row you should get the number in the first column. ur answer in b), does 47 have an inverse modulo 607, and, if so, what is it? c) [2pt] Based on vo

Answer 1

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