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Integer tuples with equal L1 and L2 norms

  1. Mar 27, 2009 #1
    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 must be a permutation of y?

    Cheers!
     
  2. jcsd
  3. Mar 27, 2009 #2
    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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