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Teachers' Lounge Discussion: Algebra

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From: Teh Oh Kian <mr_teh@hotmail.com>
To: Teacher2Teacher Public Discussion
Date: 2000121012:28:36
Subject: A special linear equation

I was told by my State Eduction Director of Education that a teacher
failed to write down the mathematical expression of the following word
problem:
Form an equation of two numbers whose sum is the multiple of their
difference.
The problem is actual simple. I tested on my son and he gave me the
equation;
x + y = k (x - y).
It's perfectly correct.
On further asking him to solve this equation, he hesitated.
It is trivial that x and y are positive integers with x > y.
On further investigation, the lower bound of y is 1 and the lower
bound of x is 2. My problem is to prove or disprove that the set of
solutions (x, y) is countably finite. If the set of feasible solutions
is countably finite, find the upper bound of x and the upper bound  y.

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