Integer tuples with equal L1 and L2 norms

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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!
 
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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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