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From: gjk@talcott.UUCP (John)
Newsgroups: net.math
Subject: Re: A simple Diophantine Equation
Message-ID: <525@talcott.UUCP>
Date: Sun, 13-Oct-85 20:36:19 EDT
Article-I.D.: talcott.525
Posted: Sun Oct 13 20:36:19 1985
Date-Received: Tue, 15-Oct-85 05:22:58 EDT
References: <364@faron.UUCP>
Distribution: net
Organization: Harvard
Lines: 16
Summary: There ain't no better way than factoring it.

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????

I don't think there is a better way.  Not only is it true that if you factor
K + AB, you get an x and a y, but also if you manage to get an x and a y
(by some other means), you get a factorization of K + AB with little addi-
tional computation.  Therefore the problems are essentially equivalent.
-- 
abcdefghijklmnopqrstuvwxyz
      ^  ^^