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Math Help - Proving that an expression is a perfect square for a finite number of values of n

  1. #1
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    Proving that an expression is a perfect square for a finite number of values of n

    Prove that is the only integer making a perfect square
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  2. #2
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    What about n=0 and n=-1?

    --Kevin C.
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  3. #3
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    True. Ok for 0 and 3 then..
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  4. #4
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    Interesting problem indeed

    Conjecture: The only integer solutions to the function f(x)=\sqrt{x^4+x^3+x^2+x+1} are (-1,1), (0,1), and (3,11). No others exist. Furthermore, \lim_{|n|\rightarrow \infty} frac(f(n))=\frac{7}{8} for n odd and \frac{3}{8} for n even, when n \in \mathbb{Z}.

    I agree, it is an interesting problem, and looking at it numerically, I believe it to be true. But why these three solutions should exist uniquely, I do not know.
    Last edited by mr fantastic; May 15th 2009 at 02:18 PM.
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  5. #5
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    UPDATE: http://www.mathhelpforum.com/math-he...duction-3.html Proof for general case found a posteriori.
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