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Integer Solutions (Posted on 2006-03-30) Difficulty: 3 of 5
Determine all integer solutions (x,y,z) for the system of equations

x²z + y²z + 4xy = 40,

x² + y² + xyz = 20

See The Solution Submitted by Bractals    
Rating: 2.5000 (6 votes)

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Question Congrats, and a question | Comment 6 of 16 |

Good job Dej and John!  After reading Jer's detailed explanation I had assumed the problem was finished.  Reading his post again I see that he left out one possibility:

(x+y)=8 (z+2)=5

which, oddly enough, would have provided the other solutions.  How unfortunate!  Are we now in agreement that those are the only solutions, or is it possible that there may be even more? 

Is there any way to know by looking at a problem like this, what the maximum number of solutions could be? 

  Posted by tomarken on 2006-03-30 16:28:17
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