Exercises
[1Z8] \(ℤ\) are the relative integers with the usual operations. Let \(p≥ 1\) a fixed integer. Consider the equivalence relation
\[ n∼ m \iff p | (n-m) \]that is, they are equivalent when \(n-m\) is divisible by \(p\).
Show that there are \(p\) equivalence classes \([0],[1],\ldots [p-1]\) We indicate the quotient space with \(ℤ/(pℤ)\) or more briefly \(ℤ_ p\).
Show that the usual operations of sum, subtraction, product in \(ℤ\) pass to the quotient.