Let n be an integer greater than 1, and let Si for
i between 1 and n-1 be a permutation over the numbers 1 through
n-1. Define Ti as follows:
T1=S1 mod n
For which values of n does such a permutation, Si, exist, where Ti is also a permutation over the numbers 1 through n-1?
For which values of n does such a permutation, Si, exist, with the further constraint that for every i, Si+Sn-i=n?
For credit, answer both questions with proof.
List of solvers:Hongcheng Zhu (1 May 13:45)
Bojan Bašić (4 May 01:59)
Mark Tilford (4 May 11:39)
Dan Dima (7 May 05:25)
Or Sheffet and Itsik Horovitz (19 May 00:12)
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