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# Show that for every number n N, n4 + 6n3 + 11n2 + 6n is divisible by 24

Show that for every number n ∈ N,
n4 + 6n3 + 11n2 + 6n is divisible by 24

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For n=1 we have p(n)= n^4+6n^3+11n^2+6n. Now p(1)=24 which is clearly divisible by 24. Now, assume that p(k)=k^4+6k^3+11k^2+6k is divisible by 24. We have to prove that p(k+1) is divisible by 24....

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