Lemma 1.
For any $x$ in the ring $F[t,t^{-1}]$ ($F[t,t^{-1}]$: the polynomials in $t$ and $t^{-1}$ with coefficients in the field $F$), $x$ is a power of $t$ if and only if $x$ divides $1$ and $t-1$ divides $x-1$ (the divisibilities are meant, of course, in $F[t, t^{-1}]$).
Lemma 2.
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@Raphael there is no crossposting mechanism. chat serves a general purpose. you yourself have advocated a crossposting mechanism. which is basically a lost cause, even nearly tilting at windmills. afaik/ afaict se mgt has never expressed any support whatsoever for the idea, and in fact has expressed signfiicant opposition. moreover it appears there have not been any major/ significant changes in se software in years. mary's questions are generally on topic wrt CS.
Lemma 1.
For any $x$ in the ring $F[t,t^{-1}]$ ($F[t,t^{-1}]$: the polynomials in $t$ and $t^{-1}$ with coefficients in the field $F$), $x$ is a power of $t$ if and only if $x$ divides $1$ and $t-1$ divides $x-1$ (the divisibilities are meant, of course, in $F[t, t^{-1}]$).
Lemma 2.
...
