ABSTRACT Let x 1,..., x n and y 1,..., y n be nonnegative numbers. If the l p -norm of (x 1,..., x n ) coincides with that of (y 1,..., y n ) for n different values of p > 0, then the x i are a permutation of the x i. This generalizes a well-known algebraic result which concerns the exponents p = 1,..., n.¶Some consequences as well as some generalizations to infinite sequences and to functions are also discussed.
