Timeline for Minimal $n$ such that $(a-1)^m | a^n - 1$ for a given $a,m > 1$

10 events

when toggle format	what		by	license	comment
Jan 25, 2018 at 15:12	vote	accept	Bryan Bush
Jan 25, 2018 at 15:04	history	edited	Max Alekseyev	CC BY-SA 3.0	added 58 characters in body
Jan 25, 2018 at 15:02	comment	added	Max Alekseyev		@FedorPetrov: Yes, I forgot to enforce $n$ be even. Thanks!
Jan 25, 2018 at 14:45	comment	added	Fedor Petrov		Your final expression still may be non integral, it should be $(a-1)^{m-1}2^{\max(2-m,-k)}$.
Jan 25, 2018 at 14:35	history	edited	Max Alekseyev	CC BY-SA 3.0	deleted 5 characters in body
Jan 25, 2018 at 14:26	history	edited	Max Alekseyev	CC BY-SA 3.0	deleted 157 characters in body; added 12 characters in body
Jan 25, 2018 at 14:25	comment	added	Max Alekseyev		@FedorPetrov: Indeed, this was my oversight. $2n$ was considered to enable the application of LTE.
Jan 25, 2018 at 14:20	comment	added	Fedor Petrov		If $a$ is odd and $(a-1)^2$ divides $a^n-1=(a-1)(1+a+\dots+a^{n-1})$, then $n$ is of course even and moreover divisible by $a-1$. And why do you care on $a^{2n}-1$ at all?
Jan 25, 2018 at 13:26	history	edited	Max Alekseyev	CC BY-SA 3.0	deleted 38 characters in body
Jan 25, 2018 at 13:19	history	answered	Max Alekseyev	CC BY-SA 3.0