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Bob and Alice make a poor choice (Posted on 2017-08-11) Difficulty: 3 of 5

Factor the semiprime:

4069102376343910986355021110116130565225765903463275841

No Solution Yet Submitted by broll    
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Solution 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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