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Dec 20, 2022 at 21:24 comment added Sidharth Ghoshal strange, i did some experimental lookup and a lot of numbers to the power 8 are 1 mod 255. I wonder why that is: [1, 2, 4, 8, 13, 16, 19, 26, 32, 38, 43, 47, 49, 52, 53, 59, 64, 67, 76, 77, 83, 86, 89, 94, 98, 101, 103, 104, 106, 118, 121, 127, 128, 134, 137, 149, 151, 152, 154, 157, 161, 166, 169, 172, 178, 179, 188, 191, 196, 202, 203, 206, 208, 212, 217, 223, 229, 236, 239, 242, 247, 251, 253, 254]. Edit: its exactly 64 values
Dec 20, 2022 at 21:22 comment added Sidharth Ghoshal ah clever in general the powers of $2$ will be good candidates in general
Dec 20, 2022 at 21:05 comment added Gerry Myerson For $n=3$, we want $k^3\equiv1\bmod7$, which holds precisely for $k\equiv1,2,4\bmod7$.
Dec 20, 2022 at 21:04 history edited Sidharth Ghoshal CC BY-SA 4.0
deleted 19 characters in body
Dec 20, 2022 at 21:04 comment added Sidharth Ghoshal yes let me edit that.
Dec 20, 2022 at 21:00 comment added Gerry Myerson What does it mean to be "a carmichael number of $2^n-1$"? Do you mean, when $n$ doesn't equal $\lambda(2^n-1)$?
Dec 20, 2022 at 19:40 vote accept Manfred Weis
Dec 20, 2022 at 19:39 comment added Manfred Weis Very nice and extensive answer; I would of course appreciate if you could provide additional code.
Dec 20, 2022 at 19:14 history edited Sidharth Ghoshal CC BY-SA 4.0
code
Dec 20, 2022 at 18:54 history answered Sidharth Ghoshal CC BY-SA 4.0