Sorry. I found a way to generate trivial counterexamples.
E.g. x = [16 13 9 4]
y = [17 12 8 5]
etc.
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.
See also the example of "bigrades" in this thread. The smallest counterexample seems to be [1,5,6] = [2,3,7].