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From: andrews@yale.ARPA (Thomas O. Andrews)
Newsgroups: net.math
Subject: Re: A simple Diophantine Equation
Message-ID: <384@yale.ARPA>
Date: Mon, 14-Oct-85 20:40:34 EDT
Article-I.D.: yale.384
Posted: Mon Oct 14 20:40:34 1985
Date-Received: Tue, 15-Oct-85 08:04:32 EDT
References: <364@faron.UUCP>
Reply-To: andrews@yale-comix.UUCP (Thomas O. Andrews)
Distribution: net
Organization: Yale University CS Dept., New Haven CT
Lines: 26
Summary: 

In article <364@faron.UUCP> bs@faron.UUCP (Robert D. Silverman) writes:
>
>Does anyone know of a simple way for solving the diophantine equation:
>
>	Ax + By + xy = K  with A,B,K given?
>
>By making the substitution x' = (x + B) and y' = (y + A)  it can
>be transformed into the problem of factoring K + AB.
>
>Is there any other way of solving it????
>
>
>Bob Silverman  (they call me Mr. 9)

If,in fact, there was a nicer way to solve this problem, then one would
also be able to quickly factor K+AB.  If anyone out there has a fast algorythm
for solving this equation, I'm sure the government would like to see it. :-)
In any event, the two problems (solution of the equation and factorization)
are basically equivalent, so there can't be a much better way to solve it ....


-- 
					      Thomas Andrews

17?  My dear, what worthless, superstitious nonsense!