Question: Prove the following using proof by induction: Claim: For all integers n 2 2, 3 | (n' - 10n + 9) (i.e. n* - 10n

Prove the following using proof by induction:

Claim: For all integers n 2 2, 3 | (n' - 10n + 9) (i.e. n* - 10n + 9 is a multiple of 3). You may use (without proof) the fact that (a + b)3 = a3 + 3ab + 3ab2 + 63 for all a, be R. Proof: We shall prove this claim by induction on n. Basis step/Base case: Inductive step: Let * > be an integer. Assume as the induction hypothesis that We want to show:

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