for any positive integer n,prove that n cube - n is divisible by 6
Asked by Bholanath Beura
| 2nd May, 2012,
08:02: PM
Expert Answer:
n3-n = n(n2-1)=n(n-1)(n+1)
For any number n, either n will be even or odd, if n will be odd then n+1 will be even, so the above term will have 2 as its factor and similarly, for any three consecutive numbers, one has to be divisble by 3. So any one of above is also divisible by 3. This means that there is 2 and 3 in the factor of above number, so it has to be divisble by 6.
Answered by
| 2nd May, 2012,
10:15: PM
Kindly Sign up for a personalised experience
- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions
Sign Up
Verify mobile number
Enter the OTP sent to your number
Change