Rank-2 difference-differential Lax pairs yield a countable family of non-trivial integrals of motion for Painlevé equations in characteristic p, one per prime.
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On difference-differential Lax pairs and integrals of Painlev\'e equations in finite characteristic
Rank-2 difference-differential Lax pairs yield a countable family of non-trivial integrals of motion for Painlevé equations in characteristic p, one per prime.