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Calculus and Beyond Homework Help
Prove True/False that n^3-n is Always Divisible By 6
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[QUOTE="CheesyPeeps, post: 5751920, member: 553192"] [h2]Homework Statement [/h2] For all natural numbers n, prove whether the following is true or false: n[SUP]3[/SUP]-n is always divisible by 6. From SQA Advanced Higher Mathematics 2006 Exam Paper [h2]Homework Equations[/h2] I can choose from the following types of proof: Direct proof Proof by contradiction Proof by contrapositive Proof by induction [h2]The Attempt at a Solution[/h2] I know the statement is true, but proving it has been more difficult than I thought it would be! I tried proof by induction, but got stuck with trying to prove true for n=k+1. I then tried proving the statement true for n=2k (even number) and n=2m+1 (odd number), but again, I didn't seem to be getting anywhere. Am I along the right lines, or should I be trying something different? [/QUOTE]
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Prove True/False that n^3-n is Always Divisible By 6
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