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social security 2026 cola concerns - ECD Germany

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 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:

📌 Not always divisible by 5 (e.g., $ n = 1 $: product = 24, not divisible by 5).

📌 Not always divisible by higher powers (e.g., $ n = 1 $: product = 24, not divisible by 48).

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