If $n \equiv 2 \pmod{7}$, then find the remainder when $(n +...

Answer guidance

Correct answer: 3 Solution: If $n \equiv 2 \pmod{7}$, then $(n + 2)(n + 4)(n + 6) \equiv 4 \cdot 6 \cdot 8 \equiv 4 \cdot 6 \cdot 1 \equiv 24 \equiv \boxed{3} \pmod{7}$.