Math Question?

Posted on 2014-12-15 08:19:00 in Math by YUTARO

Consider the expression n^5 + 9n.
(a) Prove directly that n^5 + 9n is even for all n ?N .

(b) Prove by induction that n^5 + 9n is
divisible by 5 for all n ?N .

(c) Prove that for all m ? N, 2|m and 5|m if and only if 10|m.

(d) Use 5a-5c to state a new theorem about n^5 + 9n for all n ?N , and then prove your theorem.

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