Let $Z_8$ be the set of all congruence classes of integers $\text {modulo} \ 8$. Find positive integers $a,b$ such that $[a][b]=[0]$. ($[a]$ denotes the congruence class of $a$ $\text {modulo}\ 8$
First of all, I have no idea what does $[b]$ denote.
If $$[a][b]=[0]\\ a \mod 8. [b]=[0]$$. But here I am clueless and stuck.
Now if it wants to know for which positive $a,b$, we can represent $a.b\equiv0\mod 8$, as any or both of them are even. Otherwise I don't know how to solve it.
I need help to solve and any help is highly appreciated.
One example could be $$[a]\equiv 2\pmod 8 \quad\text{and}\quad [b]\equiv 4\pmod 8$$ You are looking for the zero divisors, and in $\mathbb{Z}_8$ they are the numbers that are not coprime with $8$.