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[Merged by Bors] - feat(group_theory/order_of_element): exists_pow_eq_self_of_coprime #6875

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[Merged by Bors] - feat(group_theory/order_of_element): exists_pow_eq_self_of_coprime #6875

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tb65536
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@tb65536 tb65536 commented Mar 25, 2021

If n is coprime to the order of g, then there exists an m such that (g ^ n) ^ m = g.

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@tb65536 tb65536 added awaiting-review The author would like community review of the PR awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels Mar 25, 2021
@tb65536 tb65536 added awaiting-review The author would like community review of the PR and removed awaiting-author A reviewer has asked the author a question or requested changes labels Mar 26, 2021
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awainverse approved these changes Mar 28, 2021
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This looks like a straightforward enough proof to me, unless you want to spin off an intermediate statement that for k, n coprime with 1 < k, ∃ m : ℕ, n * m % k = 1, and then just throw that into pow_eq_mod_order_of.

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That sounds like a good refactor. Also, let's not actually use unnecessary 37s. :-)

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Thanks! 🎉

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@github-actions github-actions bot added ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) and removed awaiting-review The author would like community review of the PR labels Mar 30, 2021
bors bot pushed a commit that referenced this pull request Mar 30, 2021
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feat(group_theory/order_of_element): exists_pow_eq_self_of_coprime (#…
b4ce9b7 
…6875)

If `n` is coprime to the order of `g`, then there exists an `m` such that `(g ^ n) ^ m = g`.
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bors bot commented Mar 30, 2021

Pull request successfully merged into master.

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@bors bors bot changed the title feat(group_theory/order_of_element): exists_pow_eq_self_of_coprime [Merged by Bors] - feat(group_theory/order_of_element): exists_pow_eq_self_of_coprime Mar 30, 2021
@bors bors bot closed this Mar 30, 2021
@bors bors bot deleted the exists_pow_eq_self_of_coprime branch March 30, 2021 07:31
b-mehta pushed a commit that referenced this pull request Apr 2, 2021
@tb65536 @b-mehta
feat(group_theory/order_of_element): exists_pow_eq_self_of_coprime (#…
6381c33 
…6875)

If `n` is coprime to the order of `g`, then there exists an `m` such that `(g ^ n) ^ m = g`.
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