4.4 The Greatest Common Divisor: �The Euclidean Algorithm

313706011 鄭元淇

1. The greatest common divisior �2. The least common mulitiple

Definition 4.2

Definition 4.3

Theorem 4.6

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Proof of Theorem 4.6

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gcd characteristics

gcd characteristics

Theorem 4.7

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Proof of Theorem 4.7

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Example 4.34

Example 4.34

Example 4.33

Example 4.33

Example 4.36

Example 4.38

Example 4.38

Diophantine equation丟番圖方程式: a linear equation requiring integer solutions.

Theorem 4.8

Defination 4.4 最小公倍數

Example 4.39 -1

Example 4.39 -2

Theorem 4.9

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Proof of Theorem 4.9

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Theorem 4.10