If n is an odd integer, show that n4 + 4n2 + 11 is of the form 16k.

If n is an odd integer, then it will be of the form for some integer k.

Put in the expression,

To factor out 16 from all terms, write.

Then,

Since is the product of two successive integers, it is a multiple of 2.

Therefore,

Then,

Therefore, if is odd integer, then is a multiple of 16.