Discrete hyperbolic problem

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#1235

From: Ricky Laksanadjaja
Date: Wed, 02 Jun 1999 00:00

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Hi,

Does anybody know if there is a fast algorithm to solve the following
problem?

Equation:  x^2 - y^2 = z  , where  x is a positive integer, y is a
positive integer, and  x > y, and z is a large positive integer (>200
digit number).  For a given Zt, can you find Xn, where Xn is the first
integer which is greater or equal to SQRT(Zt), i.e. Xn >= SQRT(Zt),
which gives an integer Ym, which will satisfy the above hyperbolic
equation? I can do it by testing the equation with each integer x
greater than sqrt(Zt), but it could take million years to find Xn, if Zt
is a large integer number.  Does anyone have a better solution?
Thanks...

--
Kind Regards,

Ricky Lee
Email: lricky@earthcorp.com

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From: Ricky Laksanadjaja <lricky@earthcorp.com>
Subject: Discrete hyperbolic problem
Date: 1999/06/02
Message-ID: <37558EA7.D17E1699@earthcorp.com>
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