Integer Pythagoras

Number Theory

You have a right triangle that has integer sides. Read the following statements about that triangle:

$[1]$ At least one of the sides of that triangle must be divisible by $3$ .
$[2]$ At least one of the sides of that triangle must be divisible by $4$ .
$[3]$ At least one of the sides of that triangle must be divisible by $5$ .

Which of these statements is(are) correct?

Note: This problem is a part of this set.