U(m) is the group of positive integers j β€ m such that gcd(j, m) = 1, under multiplication modulo m.
Since elements in u(2n) are coprime to 2,
U(2n)=1,3,5...2nβ3,2nβ1 }The order
u(2n) is Ο(2n)=2nβ1,
2nβ1 is of order 2, since
(2nβ1)2=22nβ2n+1β‘1mod2nAlso(2nβ1+1)2=22nβ2+2n+1β‘1mod2nMoreso(2nβ1β1)2=2nβ2β2n+1β‘1mod2nfornβ₯3
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