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Introduction to P.M.I

The product of three consecutive natural numbers is divisible by 


Let n,n+1,n+2 be there consecutive natural number and let P(n) be their product. Then,


We have

P(1)=1×2×3=6 which is divisible by 3 and 6

P(2)=2×3×4=24, which is divisible by 3, 8 and  6

P(3)=3×4×5=60 which is divisible by 3 and 6.

P(4)=4×5×6=120 which is divisible by 3, 8 and 6.

Hence, P(n) is divisible by 6 for all n  N

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