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| The Sum of Fourth Powers (Posted on 2007-07-04) |
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Find all integer solutions to x4+y4=(x+y)(xy+1) with x≥y≥0.
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Submitted by Brian Smith
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Rating: 4.0000 (1 votes)
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Solution:
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Assume that x >= 3, then:
x^4 > x^3 + x^3 + x + x
x^4 > x^2*y +x*y^2 + x + y
x^4 + y^4 > x^2*y +x*y^2 + x + y
This contradicts the given equation, therefore 3 > x.
The potential solutions are then limited to (0,0),(1,0),(2,0)(1,1),(2,1), and (2,2).
Of these possibilites only (0,0) and (1,0) are solutions.
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Comments: (
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Subject |
Author |
Date |
 | Solution | hoodat | 2007-07-04 19:16:36 |
| Solution | K Sengupta | 2007-07-04 14:49:31 |
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