Question

Number of prime factor of $2^{14}+1$ is

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is B $3$

$(2^7+1{)}^2=2^{14}+2\cdot 2^7+1\Rightarrow (2^7+1{)}^2-2^8=2^{14}+1\Rightarrow 2^{14}+1=(2^7+1+2^4)(2^7+1-2^4)$
$=145\times 113=5\times 29\times 113$