For mathematical proofs, I want to be able to find all integers that divide another integer. For instance, integers that divide 50.
Following the definition that:
- $a$ and $b$ are integers where $b$ not equal to $0$
- $a$ is divisible by $b$ ($a/b$), if there is another integer $c$ where $a = bc$
In the example above. I could say that 50 is divisible by 5 since $10\times5=50$ satisfying $a = bc$. But how can I prove it for all integers using the previous definition? Or am I looking at the wrong thing?