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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
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(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
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Require Export Zpower.
Local Open Scope Z_scope.
(** Properties of the power function over [Z] *)
(** Nota: the usual properties of [Z.pow] are now already provided by [BinInt.Z]. Only remain here some compatibility elements, as well as more specific results about power and modulo and/or primality. *)
Proof (Z.pow_1_r x).
Notation Zpower_nat_Zpower := Zpower_nat_Zpower (only parsing).
(** * Z.pow and modulo *)

Theorem Zpower_mod p q n :
0 < n -> (p^q) mod n = ((p mod n)^q) mod n.