Sorry if this is a bad question but I was asked to prove the rules for exponents (such as a^x*a^y = a^(x+y)) but I didn't quite understand the notation our professor used.
He says to "Deduce those laws for elements α ∈ Z/mZ and k1, k2 ∈ Z≥0."
I'm not quite sure what he means by Z/mZ. I googled it and all I could figure out was that it has something to do with the modulus operator. Thanks!
It does have to see with moduli: $\mathbf Z/m\mathbf Z$ is the set of (classes of congruence of) integers modulo $m$. $m\mathbf Z$ denotes the set of multiples of $m$, and two integers are congruent modulo $m$ if their difference is an element of $m\mathbf Z$.
By the algorithm of Euclidean division, this also means $a$ and $b$ have the same remainder upon division by $m$.