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anonymous

  • 4 years ago

2013 + k is a perfect square . Find all the possible values of k.

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  1. Mr.Math
    • 4 years ago
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    You want to find all values of k such that \(2013+k=n^2 \implies k=n^2-2013\), which has infinitely many solutions over the integers. Thus there are infinitely many k such that \(2013+k\) is a perfect square.

  2. dumbcow
    • 4 years ago
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    x^2 = 2013 + k -> k = x^2 -2013, for all integers x>0

  3. anonymous
    • 4 years ago
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    k>=-2013

  4. anonymous
    • 4 years ago
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    and the smallest k is =-2012

  5. anonymous
    • 4 years ago
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    k=-2013 is that possible?

  6. anonymous
    • 4 years ago
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    (a+b+c)^2 = (2013 + k) is the original equation.

  7. anonymous
    • 4 years ago
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    are we looking for solution in R or C?

  8. anonymous
    • 4 years ago
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    In integers.

  9. anonymous
    • 4 years ago
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    Mr. Math and dumbcow seem right..

  10. anonymous
    • 4 years ago
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    a,b,c are also integers?

  11. anonymous
    • 4 years ago
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    yes

  12. EarthCitizen
    • 4 years ago
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    there should be only two values of k ?

  13. anonymous
    • 4 years ago
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    no,you are supposed to find all the possible values .

  14. anonymous
    • 4 years ago
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    all possible values seem infinite..

  15. anonymous
    • 4 years ago
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    1 more condition : a^ + 2bc = 2012, b^2 + 2ca = 1,c^2 + 2ab = k.

  16. anonymous
    • 4 years ago
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    (:

  17. Mr.Math
    • 4 years ago
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    Lol, Could your write the whole problem so we can help?

  18. anonymous
    • 4 years ago
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    If a, b, c are integers such that a^ + 2bc = 2012, b^2 + 2ca = 1,c^2 + 2ab = k.Then,find all the possible values of k.

  19. anonymous
    • 4 years ago
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    \[ac \le0 \qquad a \le0 \quad or \quad c \le0\]

  20. anonymous
    • 4 years ago
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    is there any options?

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