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Example: | Example: | ||
Prove that <math> \forall n\in{\mathbb N}, n^5-n </math> is a multiple of n. | Prove that <math> \forall n\in{\mathbb N}, n^5-n </math> is a multiple of n. | ||
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| + | Base case: n=0... 0^5=0 as we want | ||
| + | |||
| + | Inductive step: Assume that 5 divides n^5-n and show that 5 divides (n+1)^5-(n+1) | ||
Revision as of 14:36, 7 September 2008
Example: Prove that $ \forall n\in{\mathbb N}, n^5-n $ is a multiple of n.
Base case: n=0... 0^5=0 as we want
Inductive step: Assume that 5 divides n^5-n and show that 5 divides (n+1)^5-(n+1)
