a) Show that n(2n + 1)(7n + 1) is divisible by 6 for all integers n.
b) Find all integers n such that n(2n + 1)(7n + 1) is divisible by 12.
Please put only one question per post.
a) I would prove this using induction. I will outline the method here.
Show true for n=0
Assume true for n=k where k is some integer.
then prove that it will be true for n=k+1 (I've done this myself so I know it works)
Assume true for n=k
Prove it is true for n=k-1
Step 4. (Summary)
Since it is true for n=0 it must be true for n=1, n=2 .......etc
also, since it is true for n=0 it must be true for n=-1, n=-2 ..... etc
Therefore it must be true for all integer values of n.
Now try filling in the blanks.