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jmc

number theory junior

Problem

If

n \equiv 2 (mod 7)

, then find the remainder when

(n + 2) (n + 4) (n + 6)

is divided by 7.

Solution

If

n \equiv 2 (mod 7)

, then

(n + 2) (n + 4) (n + 6) \equiv 4 \cdot 6 \cdot 8 \equiv 4 \cdot 6 \cdot 1 \equiv 24 \equiv 3 (mod 7)

.

Final answer

3