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Let n>1 be an integer, let S be the set of numbers
{0, 1, ... , n-1} and let A, B and C be
one-to-one functions to and from S.
Part 1: The Addition ProblemFor which values of n is it possible to find such A, B and C satisfying that for all x in S, A(x)+B(x)=C(x) (mod n)?Part 2: The Multiplication ProblemFor which values of n is it possible to find such A, B and C satisfying that for all x in S, A(x)*B(x)=C(x) (mod n)?Bonus Question: The Power ProblemFor which values of n is it possible to find such A, B and C satisfying that for all x in S, A(x)B(x)=C(x) (mod n)?Note for the last part that 00 is not defined. In order to be considered a solver for any of the parts, you should provide for each n either an example for such A, B and C or proof that such A, B and C do not exist. A separate list of solvers will be kept for each of the two parts. Answer either or both. |
List of solvers:Part 1:Ross Millikan (6 December 04:17)David Jager (6 December 23:20) Wolfgang Kais (9 December 23:15) Dan Dima (14 December 08:11) Rick Kaye (14 December 18:04) Ananda Raidu (31 December 20:34) Mark Tilford (1 January 01:43) Both parts:Omer Angel (1 December 05:25)Oded Margalit (17 December 11:16) Itsik Horovitz (18 December 20:59) Hongcheng Zhu (19 December 22:54) Albert Stadler (20 December 20:29) Bojan Bašić (23 December 23:22) Rani Hod (26 December 23:39) |
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