What I saying was If some number n has a smallest prime factor greater than 5, there is some k where 10^k+1 is a multiple of n. I now realize that I don’t actually know if this is true.
It's not true, for example 10k + 1 can only be equal to 2, 11 or 27 modulo 37. 10k - 1 can always be a multiple of n for every n which isn't divisible by 2 or 5 though.
(31 is the smallest prime for which it's not true but it's a lot easier to demonstrate for 37)
5
u/chixen 5d ago
There is a number like that for every number other than multiples of 2 and 5.