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Integer Solutions (Posted on 2006-03-30)

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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Solution

| Comment 10 of 16 |

I got z = 20/y^2-2 with x = y.

Since the only integer solutions of 20/y^2 are y^2 = 1 and y^2 = 4, this shows that the 4 answers found are unique.

Posted by goFish on 2006-03-31 06:43:27

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