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## Equidistribution

Prove that if $(\xi_n)$ is a sequence of real numbers such that the fractional parts of $\xi_{n+h}-\xi_n$ are equidistributed in $[0,1]$ for every positive integer $h$, then the fractional parts of $\xi_n$ are also equidistributed in $[0,1]$.

Use this to prove that if $P$ is a non-constant polynomial with real coefficients, with at least one of these coefficients irrational, then the fractional parts of $P(n)$ are equidistributed in $[0,1]$.