perfect shuffle of 2n cards - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T13:36:48Z http://mathoverflow.net/feeds/question/93024 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/93024/perfect-shuffle-of-2n-cards perfect shuffle of 2n cards BenJammin 2012-04-03T18:26:48Z 2012-04-03T18:42:28Z <p>permutation is given by f(i) = 2i if i&lt;=n and 2(i-n)-1 if i>n</p> <p>where i denotes the position of cards. eg pack of cards (1,2,3,4)-->(3,1,4,2)</p> <p>Basically trying to find the multiplicative order of 2 mod(2n+1) got pretty far with for special cases such as 2n+1 being prime.</p> <p>if 2n+1 = 2^k+1 then order = 2k</p> <p>if 2n+1 = 2^k-1 then order = k</p> <p>if 2n+1 = 2m+1 where m prime and m=3(mod4) then order = m</p> <p>i thought the rest would have order = 2n by fermats little theoram but when 2n+1=103 this is not the case (it has order 51)</p> <p>any help would be much appreciated</p> http://mathoverflow.net/questions/93024/perfect-shuffle-of-2n-cards/93027#93027 Answer by Robert Israel for perfect shuffle of 2n cards Robert Israel 2012-04-03T18:42:28Z 2012-04-03T18:42:28Z <p>See <a href="https://oeis.org/A002326" rel="nofollow">https://oeis.org/A002326</a> and references there.</p>