Use the extended Euclidean algorithm to find the greatest common divisor of 13,661 and 1,558 and express it as a linear combination of 13,661 and 1,558. Step 1: Find 91 and ₁ so that 13,661 = 1,558 91 + ₁, where 0 ≤ r₁ < 1,558. - 1,558.91 = Then 1 = 13,661 Step 2: Find 12 and 12 so that 1197 1,558 = ₁ 92 +2, where 0 ≤ 2<^1. Then 2 = 1,558 – 1197 92 = 361 Step 3: Find 93 and 3 so that 1 = 2 93 +131 where 0 ≤3<г2° = 1197 361 93 = 114 Then 3 Step 4: Find 94 and 14 so that 2=3 94 + "4' Then 4 = 361 where 0 ≤4<"3. - 114 Step 5: Find and 15 5 so that 3 = 11° 95 +5, where 0 ≤ 5 < 4. Then 5 = 114 19 ). . 94 19 95 0 Step 6: Conclude that gcd (13661, 1558) equals which of the following. ○ gcd (13661, 1558) = 4 - 5 93 gcd (13661, 1558) = 12 - 4·95 gcd (13661, 1558) = 2 - gcd (13661, 1558) = ○ gcd (13661, 1558) = 3 94 3 -14·95 ₁ −2⋅ 94 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 where s = gcd (13661, 1558) = 13,661s + 1,558t, and t = Need Help? Read It

Use the extended Euclidean algorithm to find the greatest common divisor of 13,661 and 1,558 and express it as a linear combination of 13,661 and 1,558. Step 1: Find 91 and ₁ so that 13,661 = 1,558 91 + ₁, where 0 ≤ r₁ < 1,558. - 1,558.91 = Then 1 = 13,661 Step 2: Find 12 and 12 so that 1197 1,558 = ₁ 92 +2, where 0 ≤ 2<^1. Then 2 = 1,558 – 1197 92 = 361 Step 3: Find 93 and 3 so that 1 = 2 93 +131 where 0 ≤3<г2° = 1197 361 93 = 114 Then 3 Step 4: Find 94 and 14 so that 2=3 94 + "4' Then 4 = 361 where 0 ≤4<"3. - 114 Step 5: Find and 15 5 so that 3 = 11° 95 +5, where 0 ≤ 5 < 4. Then 5 = 114 19 ). . 94 19 95 0 Step 6: Conclude that gcd (13661, 1558) equals which of the following. ○ gcd (13661, 1558) = 4 - 5 93 gcd (13661, 1558) = 12 - 4·95 gcd (13661, 1558) = 2 - gcd (13661, 1558) = ○ gcd (13661, 1558) = 3 94 3 -14·95 ₁ −2⋅ 94 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 where s = gcd (13661, 1558) = 13,661s + 1,558t, and t = Need Help? Read It

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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