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Home » So $ 12 \mid (n - 1)(n + 1) $. - Network4

So $ 12 \mid (n - 1)(n + 1) $. - Network4

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 t^2 + 5t + 6 = (t + 2)(t + 3)

📌 S(t) = rac{(t + 2)(t + 3)}{t + 2}

📌 eq -2 $, we can cancel $ t + 2 $:

📌 S(t) = t + 3

📌 Now, we are to find the smallest integer value of $ t $ such that $ S(t) $ is an integer. Since $ S(t) = t + 3 $ for all $ t

📌 eq -2 $, and $ t + 3 $ is always an integer when $ t $ is an integer (except at $ t = -2 $, where the function is undefined), the smallest integer $ t $ for which $ S(t) $ is defined and an integer is the smallest integer greater than $-2$, which is $ t = -1 $.

📌 Evaluate $ S(-1) $:

📌 S(-1) = -1 + 3 = 2

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