Why n cubed minus n is divisible by 6
Why n cubed minus n is divisible by 6
IP 1
7 marks
- Factorise \(n^3-n\) completely.[2]
- Explain why \(n^3-n\) is divisible by \(6\) for every positive integer \(n\).[3]
- Hence, without using a calculator, find the value of \(101^3-101\) and show that it is divisible by \(600\).[2]
Solution:
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Answer:(a) \(n(n-1)(n+1)\) (b) three consecutive integers include a multiple of \(2\) and a multiple of \(3\) (c) \(1\,030\,200=600\times1717\)
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