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Title: Euclid's Algorithm
Description: 10 pages. Euclid's Algorithm: Definitions, theorems with proofs and examples.
Description: 10 pages. Euclid's Algorithm: Definitions, theorems with proofs and examples.
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Proposition: Let a, b be two integers, not both zero and let k Z
then:
CommDiv(a,b) = CommDiv(b, a-kb)
Theorem: (Euclid's Algorithm) Let a and b be two non zero
integers
...
Then (a:b)=r the least non
zero reminder
...
Then there exist two integers s, t such that
(a:b) = sa + tb
Observation: Let a, b Z not both zero and c Z
...
The
following assertions are equivalent:
1- d|a and d|b and if c|a and c|b then c < d
...
3- d|a and d|b and if c|a and c|b then c|d
...
Title: Euclid's Algorithm
Description: 10 pages. Euclid's Algorithm: Definitions, theorems with proofs and examples.
Description: 10 pages. Euclid's Algorithm: Definitions, theorems with proofs and examples.