TariqMy 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.
Sami Määttä@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.
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"
Mike McCoy@rzeta0 yes. Suppose x is a multiplicative inverse of 1, that is x*1=1. But 1 is the identity so x*1=x. Thus, x=1.
Refurio Anachro
Joana de Castro Arnaud@rzeta0 4 × 4 = 1 (mod 5), for instance. Things get weirder if the modulo isn't prime: 3 × 4 = 0 (mod 6).