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Cubic Expression Equals a Quadratic Expression (Posted on 2024-07-01)

Determine all pairs (x,y) of positive integers that satisfy this equation:

x³+y³= x²+42xy+y²

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Some solutions.

| Comment 1 of 3

Special case: suppose x=y

Then 2x^3 = 44x^2

2x^2(x - 22) = 0

which give 2 solutions, although (0,0) is disallowed since x,y > 0.

But we have one solution: (22,22)

Then by brute force (but not analytically so far),

I also found (1,7) and (7,1).

Posted by Larry on 2024-07-01 09:27:54

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