My brain's not working.

Is the multiplicative inverse of 1 modulo n always 1, and nothing else?

Of course 1*1=1 ... but I'm doubting myself and wondering if modulo arithmetic opens other possibilities.

#maths #numbertheory

@rzeta0 sorting through the cobwebs of my mind, I would say that n+1 for any integer n is the multiplicative inverse of 1 as well, since (n+1)*1 = n+1 = 1 (mod n).

But you could calculate n+1=1 (mod n) every time 'before' multiplication and get 1*1=1.

Not really sure if this is trivial in some sense at this moment.

@SamiMaatta

yes, this is the sort of thing my brain is worried about

in this case 𝑛+1≡1 modulo 𝑛 and so is considered "the same as 1"