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Marquez's Equation (Posted on 2005-03-02) Difficulty: 3 of 5
Find all postive integer solutions to the equation x^y-y^x=x+y.

See The Solution Submitted by owl    
Rating: 4.1429 (7 votes)

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re: Am I wrong ? Sorry to say. | Comment 4 of 9 |
(In reply to Am I wrong ? by pcbouhid)

You wrote:

So, [x^(y-1) - 1] = k1.(x-1) for some integer value of k1.

And [y^(x-1) - 1] = k2.(y-1) for some integer value of k2.

but k1 and k2 are polynomials.  For example if y=3, k1=(x+1).

My hope would be that since as you found an x^2 this somehow yields the two solutions we found and this additional polynomial give no others.

 


  Posted by Jer on 2005-03-07 17:04:42
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