Quote:
Originally Posted by Jacob Visser
It was covered in my first sentence :

That is only because of the way that you interpret your loose usage of the language 
Quoting directly from your text,
Quote:
The integer solutions are {1,2}, {0,3}, {2,1} and {3,0} and of course the solution [0,0]

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Clearly, that is the ONLY place where you claim any solution(s).
Further, you had stated,
Quote:
This simplifies the problem to find the integer solutions of x2+y2+xy3x3y=0 or y2+(x3)y+x23x=0

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No where do you state that it is the "OR" rather than the "AND" of the two conditions.
So, I do not think it to be a totally unreasonable reading of your statements to be that there is only one solution
Please understand that my complaint is only with the method that you chose to present the "solutions". Because of multiple possible interpretations of the words, your answer lacks clarity.