n cube + n+1 cube +n+2 cube is a multiple of 9 by mathematical induction

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Therefore, by PMI ,P(n) is true for all n N.
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Please check your question.What do we need to find in that question?
 
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I am really sorry it is asked to proof by mathematical induction
n cube + n+1 cube +n+2 cube is a multiple of 9
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What are you looking for?