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Friday, April 19, 2013

Gauss theorem

Given three integers a, b ​​and c, we have:
(a b = 1 and a | bc) a | c. 


Demonstration :
Suppose a ∧ b = 1 and a | bc. According to the Bezout identity, there are two integers u and v such that au + bv = 1, which implies acu+bcv= c.
as a | bc, a | bcv and therefore:
a | acu + bcv=c.

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