- (a) Prove by induction that, for all \(n \in \mathbb { Z } ^ { + }\)
$$\mathrm { f } ( n ) = n ^ { 5 } + 4 n$$
is divisible by 5
(b) Show that \(\mathrm { f } ( - x ) = - \mathrm { f } ( x )\) for all \(x \in \mathbb { R }\)
(c) Hence prove that \(\mathrm { f } ( n )\) is divisible by 5 for all \(n \in \mathbb { Z }\)
[0pt]
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