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

Answer:

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

Step-by-step 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, $a=2 \neq -2=b$.