Divisor of Integer/Examples/6 divides n (n+1) (n+2)/Proof 1

Proof
From $3$ divides $n \paren {n + 1} \paren {n + 2}$:
 * $3 \divides n \paren {n + 1} \paren {n + 2}$

From $2$ divides $n \paren {n + 1}$:
 * $2 \divides n \paren {n + 1}$

and so:
 * $2 \divides n \paren {n + 1} \paren {n + 2}$

Hence:
 * $2 \times 3 = 6 \divides \paren {n + 1} \paren {n + 2}$