Abstract Algebra: We show that Aut(Z/n) is isomorphic to (Z/n)*, the group of units in Z/n. In turn, we show that the units consist of all m in Z/n with gcd(m,n)=1. Using (Z/n)*, we define the Euler totient function and state and prove Fermat's Little Theorem: if p is a prime, then, for all integers k, p divides k^p - k.
U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.org/UReddit.html
Tagged under: Mathematics,abstract,algebra,group,theory,automorphism,isomorphism,modular,integer,congruence,Lagrange,Fermat,Euler,unit,ring,totient,divisor
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