Free help with homework

Why join Brainly?

  • ask questions about your assignment
  • get answers with explanations
  • find similar questions


N* (n2-1) is always divisible by 6
0 0 0
Case-1 where n is odd-
now if n=2a+1(a is any natural no.),2 divides (n+1)(n-1) again (n-1),n and (n+1) are three consecutive numbers.Hence 3 divides at least one of the three numbers-n,(n+1) and (n-1). So,3*2 or 6 divides n^3-n
Case-2 where n is even-
if n=2a(a is any natural number),2 divides n.So,2 divides n^3-n.Again, by the same logic 3 divides n^3-n.So,3*2 or 6 divides n^3-n when n is even.
Thus proved that 6 divides n^3-n .
1 5 1
The Brain
  • The Brain
  • Helper
Not sure about the answer?
Learn more with Brainly!
Having trouble with your homework?
Get free help!
  • 80% of questions are answered in under 10 minutes
  • Answers come with explanations, so that you can learn
  • Answer quality is ensured by our experts