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anonymous

  • 4 years ago

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

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  1. anonymous
    • 4 years ago
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    * (14^n + 11)/2

  2. Mr.Math
    • 4 years ago
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    The expression you gave is never integer.

  3. Mr.Math
    • 4 years ago
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    \(14^n+11\) is odd \(\forall n\in \mathbb{Z}\), which implies \(\frac{14^n+11}{2}\) is never integer and hence never prime.

  4. anonymous
    • 4 years ago
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    what about n=0?

  5. anonymous
    • 4 years ago
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    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
    • 4 years ago
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    I never thought of that!

  7. Mr.Math
    • 4 years ago
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    sorry, I was just about to change tjat\(\forall n\in \mathbb{N}\).

  8. Mr.Math
    • 4 years ago
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    It's obviously not prime for n=0, because (1+11)/2=6.

  9. anonymous
    • 4 years ago
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    Simply even+odd is odd hence the proof.

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