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Jul 13, 2021 at 0:50 comment added Yuval Peres Indeed. The underlying observation is that if $X$ and $Y$ are independent uniform elements of a finite (or compact) group $G$, then $X,Y, XY$ are three pairwise independent (but dependent) uniform variables in $G$.
Jul 12, 2021 at 7:13 comment added H A Helfgott This is essentially the same as the argument given by @RonniePavlov.
Jul 12, 2021 at 4:39 history answered Yuval Peres CC BY-SA 4.0