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Home » Le produit de deux nombres pairs consÃ©cutifs est 288. Trouvez les nombres. - Leaselab

Le produit de deux nombres pairs consÃ©cutifs est 288. Trouvez les nombres. - Leaselab

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 $ n = 1 $: $ 1^2 = 1 \equiv 1 \pmod{12} $ ✅

📌 Thus, the smallest such $ n $ is $ \boxed{1} $.

📌 Solution: Consider four consecutive integers: $ n, n+1, n+2, n+3 $.

📌 The product is $ P = n(n+1)(n+2)(n+3) $.

📌 Among any four consecutive integers, one is divisible by 4.

📌 At least two are even, so the product is divisible by $ 2^3 = 8 $.

📌 Thus, $ P $ is divisible by $ \text{lcm}(8, 3) = 24 $.

📌 We check if a larger fixed divisor is guaranteed:

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