Teacher2Teacher 
Q&A #3962 
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From: Teh Oh Kian <mr_teh@hotmail.com> To: Teacher2Teacher Public Discussion Date: 2000121011:28:36 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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