Math Help - kernel

1. kernel

Let f: (Z,+)->(Z6,+) defined by f(k)={set of k}
Find ker f?

2. Originally Posted by mathemanyak
f(k)={set of k}
You mean $f(k)=\left\{n\in\mathbb{Z}:n\equiv k\!\!\!\pmod{6}\right\}=[k]_6$.

The answer is $\{6m:m\in\mathbb{Z}\}$. I leave the proof to you.