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Math Help - Method for factoring into primes, when know the difference between factors?

  1. #1
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    Method for factoring into primes, when know the difference between factors?

    Say I have a number x=yz
    y and z primes, then if I know the difference between y and z is there a known method for then computing the values of y and z?

    I know a method for when I have phi(x) but I do not know it in this case and can't rework the formula for my other method to make it work for me.

    Any suggestion?
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  2. #2
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
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    Wellington
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    Hello,
    the method with phi is basically identical. You know that :

    yz = x
    y - z = a (a is the difference)

    This is a simple system of equations that you can solve (substitute the second one into the one and solve the quadratic). The method with phi just needs some preprocessing to obtain the difference between the factors.
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