Euler,s Factorization Method
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12-9-2020
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Euler's Factorization Method
A factorization algorithm which works by expressing
as a quadratic form in two different ways. Then
 |
(1)
|
so
 |
(2)
|
 |
(3)
|
Let
be the greatest common divisor of
and
so
(where
denotes the greatest common divisor of
and
), and
 |
(7)
|
But since
,
and
 |
(8)
|
which gives
 |
(9)
|
so we have
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