Materi Algoritma Euclid

1. The Euclidean
Alogrithm
Sugama Maskar
Mathematics Education Study Program
Faculty of Arts and Education
29/04/2019

2. Objective
Students can understand about
euclidean algorithm and
properties to find greatest
common divisor
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3. Preliminary
Find the greatest common divisor
of 30 and 72 with Theorem 3.7?
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4. (Continued) Solution
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72 = 30. 2 + 12
30 = 12. 2 + 6
12 = 6. 2 + 0

5. Thorem 3.11. The Euclidean
Algorithm
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6. continued
r0 = r1 . q1 + r2
r1 = r2 . q2 + r3
r2 = r3 . q3 + r4
:
r(j) = r(j+1) . q(j+1) + r(j+2)
n = j+1
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7. Lemma 3.3.
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8. Proof of Theorem 3.11.
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9. continued
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10. Example
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11. Euclidean Theorem in Fibonacci
Sequence
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12. Example
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13. Theorem 3.12
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14. Continued (proof)
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15. Assignment
Proof Lame’s Theorem!
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16. Thank you
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