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

1. anonymous

* (14^n + 11)/2

2. Mr.Math

The expression you gave is never integer.

3. Mr.Math

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

4. anonymous

5. anonymous

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.

6. anonymous

I never thought of that!

7. Mr.Math

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

8. Mr.Math

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

9. anonymous

Simply even+odd is odd hence the proof.