Let $m\geq 3$. Suppose that $$ 1-2^{-2^{m^24^m}}<γ<1. $$ Then the set $$ \{p\text{ prime}:\, p=[n^{\frac1γ}]\text{ for some }n\in{\mathbb N}\} $$ contains infinitely many non-trivial $m$-term arithmetic progressions.
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