Timeline for equivalence of definitions of Carmichael numbers [closed]

12 events

when toggle format	what		by	license	comment
S Dec 9, 2015 at 0:20	history	closed	Stefan Kohl♦ Ryan Budney Kim Morrison		Not suitable for this site
S Dec 9, 2015 at 0:20	comment	added	Kim Morrison		I'm closing this question as off-topic; it has been answered in the comments.
Dec 8, 2015 at 17:54	review	Close votes
Dec 9, 2015 at 0:20
Dec 8, 2015 at 16:33	answer	added	user83845		timeline score: -2
Mar 17, 2012 at 18:19	vote	accept	laerne
Mar 16, 2012 at 14:14	answer	added	laerne		timeline score: 0
Mar 15, 2012 at 14:17	comment	added	KConrad		From the condition on the right, prove n satisfies Korselt's criterion. (Look in any book that discusses Carmichael numbers for a proof.) In particular, you can write $n=p_1...p_r$ with distinct primes $p_i$. To prove two integers are congruent mod $n$, check they're congruent modulo each $p_i$. So we want to show for every $a$ that $a^n\equiv a \bmod p_i$ for all $i$. Write this as $a(a^{n−1}−1)\equiv 0 \bmod p_i$. Since $p_i−1$ is a factor of $n−1$ (by Korselt), if gcd($a$,$p_i$)=1 then $a^{n-1}\equiv 1 \bmod p_i$,and if gcd($a$,$p_i$)>1 then $p_i\|a$ so $a \equiv 0 \bmod p_i$. QED
Mar 15, 2012 at 14:08	comment	added	Emil Jeřábek		Do show that $n$ is square-free.
Mar 15, 2012 at 14:06	history	edited	Emil Jeřábek	CC BY-SA 3.0	fix
Mar 15, 2012 at 13:59	history	edited	KConrad	CC BY-SA 3.0	added 151 characters in body; added 2 characters in body; added 37 characters in body
Mar 15, 2012 at 13:51	history	edited	laerne		edited tags
Mar 15, 2012 at 13:39	history	asked	laerne	CC BY-SA 3.0