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Math Help - Integer tuples with equal L1 and L2 norms

  1. #1
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    [Solved] Integer tuples with equal L1 and L2 norms

    Dear all,

    Let x and y be n-tuples of non-negative integers. Furthermore,

    sum x_i = sum y_i

    and

    sum x_i^2 = sum y_i^2

    Is it true that x is necessarily a permutation of y?

    Thank you!

    -----------

    Sorry. I found a way to generate trivial counterexamples.

    E.g. x = [16 13 9 4]
    y = [17 12 8 5]

    etc.
    Last edited by boy_travels; March 27th 2009 at 03:56 PM.
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  2. #2
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    Sorry. I found a way to generate trivial counterexamples.

    E.g. x = [16 13 9 4]
    y = [17 12 8 5]

    etc.
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  3. #3
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    Opalg's Avatar
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    See also the example of "bigrades" in this thread. The smallest counterexample seems to be [1,5,6] = [2,3,7].
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