Question

Prove that (14^n + 4)/2 is never prime.

Answer 1

* (14^n + 11)/2

Answer 2

The expression you gave is never integer.

Answer 3

\(14^n+11\) is odd \(\forall n\in \mathbb{Z}\), which implies \(\frac{14^n+11}{2}\) is never integer and hence never prime.

Answer 4

what about n=0?

Answer 5

14^n, for n>0 will always end with a 4 or a 6.
And since 4+11 = 15 which is odd and 6+11 = 17 which is odd.
14^n + 11 will always be odd. And therefore as Mr.Math said, it won't be an integer and hence not a prime.

Answer 6

I never thought of that!

Answer 7

sorry, I was just about to change tjat\(\forall n\in \mathbb{N}\).

Answer 8

It's obviously not prime for n=0, because (1+11)/2=6.

Answer 9

Simply even+odd is odd hence the proof.