Question

Provide a counterexample:

If a and b are integers where a is divisible by b and b is divisible by a, then a = b.

Answer 1

`a=2 \quad \text{and} \quad b=-2`

Explanation:

Take
`a=2 \quad \text{and} \quad b=-2`, note that

`2=(-1)\cdot(-2)`

hence b divides a. On the other hand, we have that

`-2=(-1)\cdot2`

which tells us that a divides b. Moreover,
`a=2 \\eq -2=b`.