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


closed as off-topic by Namaste, Théophile, haqnatural, Vladhagen, Arnaud D. Jan 13 '17 at 23:23

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  • $\begingroup$ May I ask if this is a homework problem? $\endgroup$ – awllower Jan 13 '17 at 18:09
  • 1
    $\begingroup$ Try using modulo $3$ $\endgroup$ – lab bhattacharjee Jan 13 '17 at 18:10
  • $\begingroup$ no actually it is from binomial theorem $\endgroup$ – DXT Jan 13 '17 at 18:10

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


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.

  • $\begingroup$ It is odd. [space_needed] $\endgroup$ – Paolo Leonetti Jan 13 '17 at 18:26
  • $\begingroup$ I beg your pardon. $\endgroup$ – Harsh Kumar Jan 13 '17 at 18:29
  • $\begingroup$ Now it is better ;) $\endgroup$ – Paolo Leonetti Jan 13 '17 at 18:30
  • $\begingroup$ Thanks for help @PaoloLeonetti $\endgroup$ – Harsh Kumar Jan 13 '17 at 18:32

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