# What is the significance of i^Q mod P = 1 and are there any special properties to be aware of?

I'm studying UProve, and one of the fundamental components of this technology is based upon the relationship between

i^Q mod P = 1

"the relationship between" that equality and what? $\:$ –  Ricky Demer Mar 13 '13 at 23:57
It is useful, but I don't think it has a name. $\;\;$ If $Q$ is prime and $\: \text{mod}(i,P) \neq 1 \:$ and your equality holds, then "$i$ generates a subgroup of $\mathbb{Z}_P^*$ with order $Q$". $\;\;\;\;$ –  Ricky Demer Mar 14 '13 at 0:08
You should learn group theory and read en.wikipedia.org/wiki/Multiplicative_group_of_integers_modulo_n $\:$ –  Ricky Demer Mar 15 '13 at 17:49