Sunday, 16 April 2017

divisibility - Prove that for every natural n, (n2+n)(n2+2) can be divided by 6



Prove that for every natural number n, (n2+n)(n2+2) can be divided by 6.




I've noticed that (n2+n)=n(n+1) so these are two successive numbers hence one of them can be divided by two.



I suppose that I should prove that (n2+n)(n2+2) can be divided by 3 but I don't know how to do that.


Answer



Either n is divisible by 3, or n2+2=(n+1)(n1)+3 is.


No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...