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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

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

Elements Of Modern Algebra
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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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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