Noldorin
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 Feb22 awarded Peer Pressure Dec26 awarded Nice Question Sep26 comment Is Aluffi's “Algebra. Chapter 0” a good introduction to algebra? Not particularly challenging?! The exercises in Aluffi are well-known to be incredibly difficult. Sep11 comment Is Aluffi's “Algebra. Chapter 0” a good introduction to algebra? Care to elaborate which you prefer? Aug7 comment A finite abelian group whose order is divisible by 10 contains an element of order 10 Okay, thanks. Unfortunately I have a few similar question to the asker but do not have the FTAG yet however. Aug5 comment A finite abelian group whose order is divisible by 10 contains an element of order 10 How on earth does this help? Surely not all abelian groups are isomorphic to $Z_n$? Or perhaps I just haven't covered this yet in my book... Jul20 awarded Yearling Jul7 awarded Pundit Jul2 awarded Curious May25 comment Proof of existence of primitive roots Haha, yes. I completely messed up there... I could have started with $1 \equiv a^{p-1} \equiv a^{nd}$, but I don't think that gets us anywhere... eh. May25 comment Proof of existence of primitive roots Not sure what I was thinking any more, in fact. I believe it fails. :) May25 comment Proof of existence of primitive roots Oh yes. $a$ is just an arbitrary element of the group, the one with order denoted $k$. May25 comment Proof of existence of primitive roots As it happens, your proof/explanation gave me ideas, and I think I've come up with a really simple proof now. Perhaps you could kindly confirm? Using notation in my original question, suppose $k \nmid n$. Then $n = m k + r$, where $0 < r < k$. Now $1 \equiv a^n \equiv a^{mk} a^r \equiv (a^k)^m a^r \equiv a^r$, which contradicts that the order of $a$ is $k$. May25 comment Proof of existence of primitive roots Thank you, all looks good now! May25 revised Proof of existence of primitive roots deleted 4 characters in body May25 comment If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$ Easily the better answer here. May25 accepted Proof of existence of primitive roots May25 comment Proof of existence of primitive roots The website is suggesting we move this discussion to chat, but I'm happy to continue it wherever, FYI. :) May25 comment Proof of existence of primitive roots Hah. I know nothing of the life of Banach I'm afraid, but that sounds wise to me! And thank you. May25 comment Proof of existence of primitive roots It's the latter. But no worries, take your time, and enjoy your Saturday night. ;)