Tuesday, 21 October 2025

Exercise (1.3).14

Disprove the following:

$$a \mid b^2 \implies  a \mid b$$


We can disprove this with a counter example. 

Let's choose $a=4$ and $b=2$.This gives us

$$ 4 \mid 4 \implies 4 \mid 2 $$

which is false. So the given statement is not true for all integers $a,b$.