51. n(n+3)(n + 6)(n +9) Vne Nis divisible by
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∴n3−n=n(n2−1)=n(n+1)(n−1)=(n−1)n(n+1)
The above number: (n−1)n(n+1) is the product of three consecutive positive integers (n≥2) which is divisible by 3!=6
Hence, the number: n3−n is divisible by 6 for all positive integers n
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