# #[{(a+2)^n - (a+1)^n} - {(a+1)^n - (a^n)} pm 1] # is a prime number when #a# is a real number and #n# is a positive odd number. How do we proof it?

##### 2 Answers

Jun 26, 2016

#### Answer:

This proposition is false.

#### Explanation:

Consider the case

Then:

#[{(a+2)^n-(a+1)^n}-{(a+1)^n-(a^n)}+-1]#

#=[{(a+2)-(a+1)}-{(a+1)-(a)}+-1]#

#=[1-1+-1]#

#=+-1#

Neither

So the proposition is false.

Jun 26, 2016

#### Answer:

The assertion is false

#### Explanation:

where

But

being divisible for