Question: (a) Use induction to show that n^2 - n is always even. (b) Give a direct proof in one or two sentences that n^2 -

(a) Use induction to show that n^2 - n is always even.

(b) Give a direct proof in one or two sentences that n^2 - n is always even.

(c) Show that n^3 - n is always divisible by three.

(d) Is n^5 - n always divisible by 5? Explain your answer.

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