Here one approach . . .If 6 divides for all , prove for
What I have so far is: .
. . which I have worked out to: .
I know , but how to I prove 6 divides the rest?
Actually, we know that: . is divisible by 6.
. . So we are concerned with: .
Note that: .
. . This is: .
With two consecutive integers, one must be even and the other must be odd.
Hence, is even . . . Therefore, is a multiple of 6.