anonymous
  • anonymous
Prove that (14^n + 4)/2 is never prime.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
* (14^n + 11)/2
Mr.Math
  • Mr.Math
The expression you gave is never integer.
Mr.Math
  • 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.

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anonymous
  • anonymous
what about n=0?
anonymous
  • 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.
anonymous
  • anonymous
I never thought of that!
Mr.Math
  • Mr.Math
sorry, I was just about to change tjat\(\forall n\in \mathbb{N}\).
Mr.Math
  • Mr.Math
It's obviously not prime for n=0, because (1+11)/2=6.
anonymous
  • anonymous
Simply even+odd is odd hence the proof.

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