Rewrite 17x=3 (mod 53) as linear combination. b) Using Euclidean Algorithm to find the gcd(17, 53). c) Using recursive Euclidean Algorithm to express the gcd(17, 53) as a linear combination of 17 and 53. d) Using the Linear Combination you found in part c to find the multiplicative inverse of 17(mod 53). e) Using the inverse you find in part d to solve 17x=3 (mod 53)  , make sure you reduce your answer to LNR form.   You can use " = " as "".

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 34E
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a) Rewrite 17x=3 (mod 53) as linear combination.

b) Using Euclidean Algorithm to find the gcd(17, 53).

c) Using recursive Euclidean Algorithm to express the gcd(17, 53) as a linear combination of 17 and 53.

d) Using the Linear Combination you found in part c to find the multiplicative inverse of 17(mod 53).

e) Using the inverse you find in part d to solve 17x=3 (mod 53)  , make sure you reduce your answer to LNR form.  

You can use " = " as "".

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