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Prove n3+5n is divisible by 6 for all n using the PMI.

Prove n3+5n is divisible by 6 for all n using the PMI.

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Answer #1

is true

Assume that is true for

We will show that is also true

By induction assumption

We also have as at least one of is even

And so we must have

Therefore, is also true

And so by the PMI (principle of mathematical induction) we have

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