Let $X=\{x_1,\ldots,x_n\}$ and $Y=\{y_1,\ldots,y_n\}$ be two (equal size) sets of the complex numbers. If $\sum_{i=1}^nx_i^k=\sum_{i=1}^ny_i^k$, for all $k\geq 1$, then is this true that $X=Y$? How about if $x_i$'s and $y_i$'s are roots of unity?
Asked
Active
Viewed 44 times
1
-
Asked and answered here: https://math.stackexchange.com/q/971172/42969 – Martin R Jan 12 '22 at 14:22
-
@VeryForgetfulFunctor With $;k=2;$ the sums are not equal. – DonAntonio Jan 12 '22 at 14:23