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 Bob and Alice make a poor choice (Posted on 2017-08-11)

Factor the semiprime:

4069102376343910986355021110116130565225765903463275841

 No Solution Yet Submitted by broll No Rating

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 re: Method? | Comment 5 of 7 |
(In reply to Method? by broll)

The square root is very slightly under an integer.  This suggests the factors are close, so a difference of squares method would find the factors relatively quickly.

Specifically, there is some small value b such that the equation
4069102376343910986355021110116130565225765903463275841 = a^2 - b^2 = (a+b) * (a-b)
is solvable with integer a and b.

b=80 makes a=2017201620152014201320122079.  Then the factors are
2017201620152014201320122079 - 80 = 2017201620152014201320121999
2017201620152014201320122079 + 80 = 2017201620152014201320122159

 Posted by Brian Smith on 2017-08-11 23:30:26

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