Use the extended Euclidean algorithm to find the greatest common divisor of 9,090 and 936 and express it as a linear combination of 9,090 and 936. Step 1: Find ₁ and ₁ so that 9,090 = 936 9₁+₁, where 0 ≤r₁ < 936. Then 1 = 9,090 - 936 9₁ = Step 2: Find 92 and r₂ so that 936 = ₁.9₂ +r₂, where 0≤r₂ <1 Then = 936- 2 •92 Step 3: Find 93 and r3 so that r₁ = r₂ 93 +r3, where 0≤r3

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 59RE
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Use the extended Euclidean algorithm to find the greatest common divisor of 9,090 and 936 and express it as a linear combination of 9,090 and 936.
Step 1: Find ₁ and ₁ so that
9,090 = 936 9₁+₁, where 0 ≤r₁ < 936.
Then 1 = 9,090 - 936 9₁ =
Step 2: Find 92 and r₂ so that
936 = ₁.9₂ +r₂, where 0≤r₂ <1
Then
= 936-
2
•92
Step 3: Find 93 and r3 so that
r₁ = r₂ 93 +r3, where 0≤r3 <r₂.
Then 3
=
Step 4: Find 94 and r4 so that
r₂ = 73 94 +r4, where 0≤r4 <r3.
Then r4 =
Step 5: Find 95 and r so that
r3 = 74 95 +r5, where 0 <r5 <r4'
Then s
=
• 95 =
Step 6: Conclude that gcd (9090, 936) equals which of the following.
O gcd (9090, 936) = r₂-394
O gcd (9090, 936) = 4593
O gcd (9090, 936) = r₂-495
O gcd (9090, 936) = ₁₂94
O gcd (9090, 936) = 3495
Conclusion: Substitute numerical values backward through the preceding steps, simplifying the results for each step, until you have found numbers s and t so that
gcd (9090, 936) = 9,090s + 936t,
where s =
and t =
93
94 =
Transcribed Image Text:Use the extended Euclidean algorithm to find the greatest common divisor of 9,090 and 936 and express it as a linear combination of 9,090 and 936. Step 1: Find ₁ and ₁ so that 9,090 = 936 9₁+₁, where 0 ≤r₁ < 936. Then 1 = 9,090 - 936 9₁ = Step 2: Find 92 and r₂ so that 936 = ₁.9₂ +r₂, where 0≤r₂ <1 Then = 936- 2 •92 Step 3: Find 93 and r3 so that r₁ = r₂ 93 +r3, where 0≤r3 <r₂. Then 3 = Step 4: Find 94 and r4 so that r₂ = 73 94 +r4, where 0≤r4 <r3. Then r4 = Step 5: Find 95 and r so that r3 = 74 95 +r5, where 0 <r5 <r4' Then s = • 95 = Step 6: Conclude that gcd (9090, 936) equals which of the following. O gcd (9090, 936) = r₂-394 O gcd (9090, 936) = 4593 O gcd (9090, 936) = r₂-495 O gcd (9090, 936) = ₁₂94 O gcd (9090, 936) = 3495 Conclusion: Substitute numerical values backward through the preceding steps, simplifying the results for each step, until you have found numbers s and t so that gcd (9090, 936) = 9,090s + 936t, where s = and t = 93 94 =
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