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 ofn 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 ofn 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 ofn 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 0
In order to be considered a solver for any of the parts, you should
provide for each
A separate list of solvers will be kept for each of the two parts.
Answer |
## 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) |

Elegant solutions can be submitted to the puzzlemaster at __riddlesbrand.scso.com__.
Names of solvers will be posted on this page. Notify if you don't want
your name to be mentioned.

The solution will be published at the end of the month.

Enjoy!