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if $10^n+3(4^{n+2})+5$ is a prime number, then which one is true for $n$

(a) $9$

(b) $5$

(c) $11$

(d) $14$

could some help me with this, thanks

  • 0
    May I ask if this is a homework problem? – 2017-01-13
  • 1
    Try using modulo $3$ – 2017-01-13
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    no actually it is from binomial theorem – 2017-01-13

2 Answers 2

5

This is greater than $3$ and multiple of $3$. Hence it is not prime.

2

The number cannot be a prime. Since whatever the value of $n$ may be the power of $10^n+5$ is divisible by $3$ hence the given number is a multiple of $3$. So, it cannot be a prime.

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    It is odd. [space_needed] – 2017-01-13
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    I beg your pardon. – 2017-01-13
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    Now it is better ;) – 2017-01-13
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    Thanks for help @PaoloLeonetti – 2017-01-13