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Always Divisible (Posted on 2007-05-20) Difficulty: 3 of 5
Prove that for every integer x, there is an integer y such that (y^2-2)/(x^4+1) is an integer.

See The Solution Submitted by Brian Smith    
Rating: 4.0000 (1 votes)

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Solution Solution | Comment 2 of 3 |
This y works:

y=x^3-x

y^2 - 2 =
x^6 - 2x^4 + x^2 - 2 =
(x^4 + 1)*(x^2 - 2)

-- Joel

  Posted by Joel on 2007-05-21 02:58:29
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