(2) (b) (c) Use the Euclidean algorithm to determine the gcd of 85 Write down all the divisors of 85 and 135, and use it to determine the god directly, hence verifying the computation using the Euclidean algorithm. Find r and s such that 85r+135s = gcd. Find all the solutions to the Diophantine equation 85m + 135n = 30. and 135.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.2: Properties Of Division
Problem 51E
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(2) (a)
(b)
(c)
(d)
and 135.
determine
Euclidean
Use the Euclidean algorithm to determine the gcd of 85
Write down all the divisors of 85 and 135, and use it to
the gcd directly, hence verifying the computation using the
algorithm.
Find r and s such that 85r+ 135s = gcd.
Find all the solutions to the Diophantine equation
85m + 135n = 30.
Transcribed Image Text:(2) (a) (b) (c) (d) and 135. determine Euclidean Use the Euclidean algorithm to determine the gcd of 85 Write down all the divisors of 85 and 135, and use it to the gcd directly, hence verifying the computation using the algorithm. Find r and s such that 85r+ 135s = gcd. Find all the solutions to the Diophantine equation 85m + 135n = 30.
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